Question

solve ((x + 2)^2 = 64) using square roots. select the solution(s).

□ (x = -10) □ (x = -5) □ (x = -1) □ (x = 3)
□ (x = -8) □ (x = -4) □ (x = 0) □ (x = 4)
□ (x = -7) □ (x = -3) □ (x = 1) □ (x = 5)
□ (x = -6) □ (x = -2) □ (x = 2) □ (x = 6)

Explanation:

Step1: Take square roots of both sides

To solve \((x + 2)^2 = 64\), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution. So, \(\sqrt{(x + 2)^2}=\pm\sqrt{64}\). This simplifies to \(x + 2=\pm8\).

Step2: Solve for x in both cases

Case 1: When we take the positive square root

If \(x + 2 = 8\), we subtract 2 from both sides to solve for \(x\). So, \(x=8 - 2=6\).

Case 2: When we take the negative square root

If \(x + 2=-8\), we subtract 2 from both sides. So, \(x=-8 - 2=-10\).

Answer:

\(x = - 10\), \(x = 6\) (i.e., the options with \(x=-10\) and \(x = 6\))