How do you solve x^2+15x+56=0?

1 Answer
Mar 27, 2016

x = -7 or x = -8

Explanation:

Find a pair of factors of 56 with sum 15.

The pair 7, 8 works in that 7*8 = 56 and 7+8=15

Hence:

0 = x^2+15x+56 = (x+7)(x+8)

So:

x = -7 or x = -8

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Alternative method

I will use the difference of squares identity:

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

with a=(2x+15) and b=1 as follows:

First multiply the whole equation by 4 (to cut down on the use of fractions) to get:

0 = 4x^2+60x+224

=(2x+15)^2-225+224

=(2x+15)^2-1^2

=((2x+15)-1)((2x+15)+1)

=(2x+14)(2x+16)

=(2(x+7))(2(x+8))

=4(x+7)(x+8)

Hence x = -7 or x = -8