Question

Solve for x in the equation x^2+20x+100=36

a).x = –16 or x = –4
b).x = –10
c).x = –8
d).x = 4 or x = 16

Answer 1

a

Explanation:

Given

x² + 20x + 100 = 36 ( subtract 36 from both sides )

x² + 20x + 64 = 0 ← in standard form

Consider the factors of the constant term ( + 64) which sum to give the coefficient of the x- term ( + 20)

The factors are + 16 and + 4, since

16 × 4 = + 64 and 16 + 4 = + 20, hence

(x + 16)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 16 = 0 ⇒ x = - 16

x + 4 = 0 ⇒ x = - 4