Question

Solve x2 + 14x = −24 by completing the square. What is the solution set of the equation? {−12, −2} {−7, 7} {−6, −4} {−5, 5}

Answer 1

x² + 14x = -24

Add (b/2)²:

x² + 14x + (14/2)² = -24 + (14/2)²

x² + 14x + 7² = -24 + 7²

Complete the square:

(x + 7)² = 25

Square root both sides:

x + 7 = ±√25

x + 7 = ±5

Apply zero-product property:

x = 5 - 7 or x = -5-7

x = -2 or x = -12

Answer: [ -12 , -2]