Question

Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?

(negative 5 minus StartRoot 34 EndRoot comma negative 5 + Startroot 34 EndRoot)
(negative 5 minus StartRoot 29 EndRoot comma negative 5 + StartRoot 29 EndRoot)
{–12, 2}
{–2, 12}

Answer 1

x^2 + 10x = 24
Add 25 (half of 10 squared) to both sides: x^2 + 10x + 25 = 24 + 25
(x + 5)^2 = 49
x + 5 = ±7 → x = -5 ± 7 → x = 2 or x = -12

Solution set: {–12, 2}