Question

solve for ( x ). express your answer in simplest radical form if necessary.( x^2 = 81 )

Explanation:

Step1: Take square root of both sides

To solve for \( x \) in the equation \( x^2 = 81 \), we take the square root of both sides. The square root of a number \( y \) is a value \( z \) such that \( z^2 = y \). So, taking the square root of both sides gives us \( \sqrt{x^2} = \sqrt{81} \).

Step2: Simplify both sides

Simplifying the left side, \( \sqrt{x^2} = |x| \) (the absolute value of \( x \) because the square root of a square is the absolute value of the original number). Simplifying the right side, \( \sqrt{81} = 9 \) because \( 9^2 = 81 \) and also \( (-9)^2 = 81 \). So we have \( |x| = 9 \), which means \( x = 9 \) or \( x = -9 \).

Answer:

\( x = 9 \) or \( x = -9 \) (or can be written as \( x = \pm 9 \))