Question

Given (x – 7)^2 = 36, select the values of x. (choose 2 or more)

x=13
x=1
x=-29
x=42

Answer 1

x=13

x=1

Explanation:

(13-7)^2

Calculate any addition or subtraction, from left to right.

(13-7)^2

(6)^2

Simplify exponents and square roots

6^2

36

(1-7)^2

Calculate any addition or subtraction, from left to right.

(1-7)^2

(-6)^2

Simplify exponents and square roots

-6^2

36

Answer 2

x = 13

x = 1

Explanation:

Some equations can have multiple values for x.

Square Root

To solve for x, we need to remove the exponent. Through properties of equality and square root properties, we can manipulate the equation and isolate the variable. First, square root both sides of the equation.

• (x - 7) = ±6

When 36 is square rooted the answer is plus or minus 6. This is because both +6 and -6 equal 36 when squared. This is true for any constant that is square rooted.

Solving for x

Since there are 2 values on the right side, we need to set up 2 separate equations.

• x - 7 = 6
• x - 7 = -6

Then, we can solve both equations for x.

• x = 13
• x = 1

This shows that the values of x are 13 and 1. If you want to check your answer you can plug the values back into the equation. Whether you plug 13 or 1 in, you will get 36.