Question

Solve the quadratic equation.

x2 + 8x + 14 = 23
What is the smaller answer? x=
What is the larger answer? x=

Answer 1

x = - 9, x = 1

Explanation:

Given

x² + 8x + 14 = 23 ( subtract 23 from both sides )

x² + 8x - 9 = 0 ← in standard form

(x + 9)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9 ← smaller answer

x - 1 = 0 ⇒ x = 1 ← larger answer

Answer 2

smaller answer x=-9

larger answer x=1

Explanation:

`x^(2)`+8x+14=23

`x^(2)`+8x-9=0

D=64+36=100

`x_(1) =(-8+10)/(2) =1`

`x_(2) =(-8-10)/(2) =-9`

so, smaller answer x=-9

larger answer x=1