Question

What are the solutions to the quadratic equation below? x^2 + 13x +40=0

A.) x= -10 and x=4

B.) x=10 and x=4

C.) x=8 and x= -5

D.) x= -8 and x= -5

Answer 1

Solve the equation x² + 13x + 40 = 0 by factorization.

Multiply first term x² and last term 40 = 40x²

The correct pair of the terms 8x and 5x multiply to 40x² and add to 13x.

Replace the middle term 13x with 8x + 5x.

 x² + 8x + 5x + 40 = 0

Group the terms into two pairs.

(x² + 8x) + (5x + 40) = 0

Factor out x from the first group  and factor out 5 from the second group.

x(x + 8) + 5(x + 8) = 0

Factor out common term x + 8.

 (x + 8)(x + 5) = 0

Apply zero product property.

x + 8 = 0 and x + 5 = 0

x = - 8 and x = - 5

Solutions of  x² + 13x + 40 = 0 are at x = -8, -5.

So option D is correct.