Question

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

Answer 1

Answer:

(-12, 2).

Step-by-step explanation:

x^2 + 10x = 24

Divide the + 10 by 2  to give the following identity:

x^2 + 10x is equivalent to (x + 5)^2 - 25 so:

(x + 5)^2 - 25 = 24

(x + 5)^2 = 49

Taking square roots:

x + 5 = +/- 7.

x = -5 + 7 = 2

and x = -5 - 7 = -12.

Answer 2

Answer:

(- 12, 2 )

Step-by-step explanation:

Given

x² + 10x = 24

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = 24 + 25

(x + 5)² = 49 ( take the square root of both sides )

x + 5 = ± $\sqrt{49}$ = ± 7 ( subtract 5 from both sides )

x = - 5 ± 7

Hence

x = - 5 - 7 = - 12 or x = - 5 + 7 = 2

Solution is ( - 12, 2 )