How to solve x^2+5= -6?

Question

solve by factoring

Answer 1

The equation is x² + 5 = - 6.

Add 6 to each side.

x² + 5 + 6 = - 6 + 6

x² + 11 = 0

x² - (-11) = 0

x² - (i²11) = 0        [Since i² = -1]

x² - (i√11)² = 0.

Apply Difference of Two Squares : u² - v² = (u + v)(u - v).

(x + i√11)(x - i√11) = 0.

Apply Zero Product Property : If ab = 0, then either a = 0, b = 0, or both a and b equal zero.

x + i√11 = 0 and x - i√11 = 0.

x = - i√11 and x = i√11.