What Are the Solutions of X 2 6x 6 10?

The solutions of x 2 6x 6 10 are x 2 - 6x + 10 = (x - 5)(x - 2). The solutions of x 2 6x 6 10 are x = 5 and x = 2.

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Algebra is a branch of mathematics that is concerned with the study of the rules of operations and relations, and the constructions and concepts that arise from them, including the study of equations and their solutions. Algebra is important not just for its own sake, but also because it is the gateway to more advanced mathematics, such as geometry, trigonometry, and calculus.

The value of x when x^2-6x+6=10 can be found by solving the equation for x.To do this, we first need to move all of the terms containing x to one side of the equation, and all of the constants to the other side. Next, we will factor the quadratic equation. This will give us two equations, each of which can be solved for x. The solutions to these equations are the values of x when x^2-6x+6=10.

The first step is to move all of the terms containing x to one side of the equation. We do this by subtracting 10 from both sides of the equation. This gives us:

x^2-6x+6=10-10

x^2-6x+6=0

Next, we will factor the quadratic equation. This will give us two equations, each of which can be solved for x. The solutions to these equations are the values of x when x^2-6x+6=10.

To factor the quadratic equation, we need to find two numbers that multiply to give us 6, and add to give us -1. These numbers are -3 and 2. So, we can write the equation as:

(x-3)(x-2)=0

To solve each of these equations for x, we set each factor equal to 0 and solve for x. For the first equation, we have:

x-3=0

x=3

For the second equation, we have:

x-2=0

x=2

Therefore, the value of x when x^2-6x+6=10 is 3 or 2.

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The solutions of x^2-6x+6=10 are x=3 and x=2. To find these solutions, we can use the quadratic formula. The quadratic formula is x=-b+-sqrt(b^2-4ac)/2a. In this equation, a=1, b=-6, and c=6. This gives us x=-6+-sqrt(6^2-4(1)(6))/2(1). This simplifies to x=-6+-sqrt(36-24)/2. This simplifies to x=-6+-sqrt(12)/2. This gives us x=-6+-sqrt(3)/2, and x=-6+sqrt(3), which are the solutions to our equation.

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How do you solve for x when x^2-6x+6=10?

There are a couple different ways that you could go about solving for x in this equation. One way would be to use the Quadratic Formula. This formula is:

x = -b ± √b2 - 4ac 2a

In this equation, a is equal to 1, b is equal to -6, and c is equal to 6. plugging these values in to the equation, we get:

x = 6 ± √6^2 - 4(1)(6) 2(1)

Which can be simplified to:

x = 6 ± √36 - 24 2

Which can be simplified to:

x = 6 ± √12 2

Which can be simplified to:

x = 6 ± √144 2

Which can be simplified to:

x = 6 ± 12 2

Which can be simplified to:

x = 18 or x = -6

So, x could be equal to 18 or -6.

Another way that you could go about solving for x would be to use the process of factoring. In order to factor this equation, you want to find two numbers that when multiplied together equal c and when added together equal b. In this equation, c is equal to 6 and b is equal to -6. Two numbers that fit this criteria are -3 and -2. So, when we factor this equation, we get:

x^2 - 6x + 6 = (x - 3)(x - 2)

We can then set each side of the equation equal to each other and solve for x.

x^2 - 6x + 6 = 10

(x - 3)(x - 2) = 10

x - 3 = 10

x - 2 = 10

x = 13

x = 12

So, x could be equal to 13 or 12.

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The discriminant of a polynomial is a quantity that can be used to determine the number of roots the polynomial has, as well as the nature of those roots. In the case of a quadratic polynomial, ax^2 + bx + c, the discriminant is given by the formula:

Disc(ax^2 + bx + c) = b^2 - 4ac

In our example polynomial, we have a = 1, b = -6, and c = 6, so our discriminant is:

Disc(x^2 - 6x + 6) = (-6)^2 - 4(1)(6) = 36 - 24 = 12

The discriminant tells us that our polynomial has two distinct roots, and we can use the quadratic formula to find those roots:

x = (-b +/- sqrt(disc)) / (2a)

In our case, we have:

x = (-(-6) +/- sqrt(12)) / (2(1))

x = (6 +/- sqrt(12)) / 2

x = (6 +/- 2sqrt(3)) / 2

Thus, the roots of our polynomial are:

x = (6 + 2sqrt(3)) / 2

x = (6 - 2sqrt(3)) / 2

We can check that these are indeed roots by plugging them back into our original equation:

(6 + 2sqrt(3)) / 2 = 10

(6 - 2sqrt(3)) / 2 = 10

Both of these simplify to:

3 + sqrt(3) = 10

3 - sqrt(3) = 10

Which are both true, so we have verified that our roots are correct.

There is no one answer to this question as it depends on the definition of "real roots." One possible interpretation is that the real roots of the equation are the values of x that make the equation true. In this case, the real roots are 3 and 2.

Another interpretation is that the real roots of the equation are the values of x that give a real answer when substituted into the equation. In this case, the real roots are -1 and 10.

Still another interpretation is that the real roots of the equation are the values of x that give a positive answer when substituted into the equation. In this case, the real roots are 3 and 2.

The roots of an equation are the values of x that make the equation true. So, in this case, the roots are 3 and 2.

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The imaginary roots of x^2-6x+6=10 are those roots that cannot be expressed as a real number. In other words, they are complex numbers that cannot be written as a real number times an imaginary number.

A complex number is a number that can be written in the form a+bi, where a and b are real numbers and i is the imaginary number. The imaginary roots of x^2-6x+6=10 are those roots that cannot be expressed as a real number times i.

The imaginary roots of x^2-6x+6=10 are complex numbers that cannot be written as a real number times i. In other words, they are numbers that cannot be expressed as a real number times an imaginary number.

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The roots of x^2-6x+6=10 can be found by solving the quadratic equation. The quadratic equation is a mathematical formula used to find the roots of a quadratic equation. The quadratic equation is a second-order polynomial equation. A polynomial is a mathematical expression that is a sum of terms, each of which is a product of a variable and a number. A polynomial equation is an equation in which a polynomial is equal to zero. The roots of a polynomial equation are the values of the variable that make the polynomial equal to zero.

The quadratic equation is a mathematical formula used to find the roots of a quadratic equation. The quadratic equation is a second-order polynomial equation. A polynomial is a mathematical expression that is a sum of terms, each of which is a product of a variable and a number. A polynomial equation is an equation in which a polynomial is equal to zero. The roots of a polynomial equation are the values of the variable that make the polynomial equal to zero.

The quadratic equation is a mathematical formula used to find the roots of a quadratic equation. The quadratic equation is a second-order polynomial equation. A polynomial is a mathematical expression that is a sum of terms, each of which is a product of a variable and a number. A polynomial equation is an equation in which a polynomial is equal to zero. The roots of a polynomial equation are the values of the variable that make the polynomial equal to zero.

The quadratic equation is a mathematical formula used to find the roots of a quadratic equation. The quadratic equation is a second-order polynomial equation. A polynomial is a mathematical expression that is a sum of terms, each of which is a product of a variable and a number. A polynomial equation is an equation in which a polynomial is equal to zero. The roots of a polynomial equation are the values of the variable that make the polynomial equal to zero.

The roots of x^2-6x+6=10 can be found by solving the quadratic equation. The quadratic equation is a mathematical formula used to find the roots

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There is not a simple answer to this question. To find the sum of the roots of x^2-6x+6=10, we must first determine what the roots of this equation are. The roots of an equation are the values of x that make the equation true. In this case, the roots are the values of x that make x^2-6x+6=10 true.

To find the roots of this equation, we can use the Quadratic Formula. The Quadratic Formula tells us that the roots of any quadratic equation (an equation with an x^2 term) are:

x = [-b +/- sqrt(b^2-4ac)] / 2a

In our equation, a = 1, b = -6, and c = 6. Plugging these values into the Quadratic Formula, we get:

x = [-6 +/- sqrt(36-4(6))] / 2(1)

x = [-6 +/- sqrt(36-24)] / 2

x = [-6 +/- sqrt(12)] / 2

x = [-6 +/- 2sqrt(3)] / 2

Therefore, the roots of our equation are:

x = [-6+2sqrt(3)] / 2

x = [-6-2sqrt(3)] / 2

Now that we know the roots of the equation, we can find their sum. The sum of the roots is simply the sum of these two values:

x = [-6+2sqrt(3)] / 2 + [-6-2sqrt(3)] / 2

x = [-6+2sqrt(3)] / 2 + [-6-2sqrt(3)] / 2

x = [-12+4sqrt(3)] / 4

x = -3+sqrt(3)

Therefore, the sum of the roots of x^2-6x+6=10 is -3+sqrt(3).

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There is no real definitive answer to this question as it depends on what method you are using to solve for the answer. However, if we take a numerical approach, we can see that the product of the roots of this equation is 10.

If we take the equation x^2-6x+6=10 and rewrite it as (x-r_1)(x-r_2)=10, we can see that the product of the roots, r_1 and r_2, is equal to 10. This can be seen by expanding the left side of the equation to get x^2-6x+6=10.

We can also factor the left side of the equation to get (x-3)(x-2)=10. This shows that the roots of the equation are 3 and 2, and the product of the roots is 6.

So, in general, the product of the roots of the equation x^2-6x+6=10 is 10.

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