Question

(x+8)^2 = 9
(x+6)^2= -7

Explanation:

Step1: Solve \((x + 8)^2=9\)

Take square root on both sides: \(x + 8=\pm\sqrt{9}=\pm3\)
Case 1: \(x + 8 = 3\), then \(x=3 - 8=-5\)
Case 2: \(x + 8=-3\), then \(x=-3 - 8=-11\)

Step2: Solve \((x + 6)^2=-7\)

The square of a real number is non - negative. Since the right - hand side \(-7\) is negative, the equation \((x + 6)^2=-7\) has no real solutions. If we consider complex solutions, take square root on both sides: \(x+6=\pm\sqrt{-7}=\pm i\sqrt{7}\), then \(x=-6\pm i\sqrt{7}\)

Answer:

For \((x + 8)^2 = 9\), \(x=-5\) or \(x = - 11\); for \((x + 6)^2=-7\), no real solutions (complex solutions: \(x=-6\pm i\sqrt{7}\))