Which of the following are the values that are the solution of [tex]x^2+20=12 x[/tex]? Choose two correct answers.

[tex]x=10[/tex]
[tex]x=2[/tex]
[tex]x=-10[/tex]
[tex]x=-2[/tex]

Rewrite the equation in standard form: x 2 − 12 x + 20 = 0 .
Factor the quadratic expression: ( x − 10 ) ( x − 2 ) = 0 .
Set each factor to zero: x − 10 = 0 or x − 2 = 0 .
Solve for x: x = 10 or x = 2 . The solutions are x = 10 , x = 2 ​ .

Explanation

Understanding the Problem We are given the quadratic equation x 2 + 20 = 12 x and asked to find the two values of x that are solutions to this equation from the options x = 10 , x = 2 , x = − 10 , and x = − 2 .

Rewriting the Equation First, we need to rewrite the equation in the standard form of a quadratic equation, which is a x 2 + b x + c = 0 . Subtracting 12 x from both sides of the equation x 2 + 20 = 12 x , we get x 2 − 12 x + 20 = 0 .

Factoring the Quadratic Expression Now, we need to factor the quadratic expression x 2 − 12 x + 20 . We are looking for two numbers that multiply to 20 and add up to -12. The numbers -10 and -2 satisfy these conditions since ( − 10 ) × ( − 2 ) = 20 and ( − 10 ) + ( − 2 ) = − 12 .

Rewriting the Equation with Factors We can rewrite the quadratic equation as ( x − 10 ) ( x − 2 ) = 0 .

Setting Factors to Zero To find the solutions for x , we set each factor equal to zero and solve for x . So, x − 10 = 0 or x − 2 = 0 .

Solving for x Solving for x , we get x = 10 or x = 2 . Therefore, the two solutions to the quadratic equation are x = 10 and x = 2 .


Examples
Quadratic equations are used in various real-life scenarios, such as calculating the trajectory of a ball, determining the dimensions of a rectangular area given its area and perimeter, or modeling the growth of a population. For example, if you want to build a rectangular garden with an area of 20 square meters and a perimeter that requires 12 meters of fencing, you can use a quadratic equation to find the possible lengths and widths of the garden. This helps in optimizing the use of space and resources.

Answered by GinnyAnswer | 2025-07-07

The solutions to the equation x 2 + 20 = 12 x are x = 10 and x = 2 . Therefore, the correct choices from the options provided are x = 10 and x = 2 .
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Answered by Anonymous | 2025-08-12