How do you use factoring to solve this equation $x^2+x=56$ ?

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Answer 1 · 2015-05-23T09:57:17

$x^2+x=56$
$x^2+x - 56 = 0$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 1*(-56) = -56$
and
$N_1 +N_2 = b = 1$

After trying out a few numbers we get $N_1 = 8$ and $N_2 =-7$
$8*(-7) = -56$ , and $8+(-7)= 1$

$x^2+x - 56 = x^2+8x - 7x - 56$
$x(x +8) - 7(x+8)$

$(x-7)(x +8)$ is the factorised form

$color (red)(x = 7, x = -8$ are the solutions for the expression.

How do you use factoring to solve this equation x^2+x=56x^2+x=56?