Question

Solve the equation by factoring. x2+6x-16=0

a.{–2, –8}
c. {–2, 8}
b. {2, 8}
d. {–8, 2}

Answer 1

x = 2 or x = -8 (d)

Explanation:

Find two factors of 16 which differ by 6. The pair 8,2 works in that 8 × 2 = 16 and 8 - 2 = 6.

Hence we find:

`0 = x^2+6x-16 = (x+8)(x-2)`

So x = 2 or x = -8

Alternatively, complete the square then use the difference of squares identity:

`a^2-b^2 = (a-b)(a+b)`

with
`a = (x+3)` and
`b=5` as follows:

`0 = x^2+6x-16`

`=(x+3)^2-9-16`

`=(x+3)^2-25`

`=(x+3)^2-5^2`
`=((x+3)-5)((x+3)+5)`

`=(x-2)(x+8)`

Hence zeros
`x=2` and
`x=-8`

Subjects:

Algebra Quadratic Equations and Functions Comparing Methods for Solving Quadratics