Question

solve ((x - 1)^2 = 0) using square roots. select the solution(s).

(square) (x = -10) (square) (x = -5) (square) (x = -1) (square) (x = 3) (square) (x = 7)
(square) (x = -8) (square) (x = -4) (square) (x = 0) (square) (x = 4) (square) (x = 8)
(square) (x = -7) (square) (x = -3) (square) (x = 1) (square) (x = 5) (square) (x = 10)
(square) (x = -6) (square) (x = -2) (square) (x = 2) (square) (x = 6) (square) no solutions

Explanation:

Step1: Take square root of both sides

To solve \((x - 1)^2 = 0\) using square roots, we take the square root of both sides. The square root of a number squared is the absolute value of the number, but since the right - hand side is \(0\), we have \(\sqrt{(x - 1)^2}=\sqrt{0}\). This simplifies to \(|x - 1|=0\).

Step2: Solve for x

The equation \(|x - 1| = 0\) means that \(x-1 = 0\) (because the absolute value of a number is \(0\) only when the number itself is \(0\)). Solving \(x - 1=0\) for \(x\), we add \(1\) to both sides of the equation: \(x=1\).

Answer:

\(x = 1\) (the option with \(x = 1\))