How do you solve $x^2+ 15x= -36$ by factoring?

Question

1604 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-23T11:20:50

The solutions are
$color(blue)(x=-3$
$color(blue)(x=-12$

$x^2+15x=−36$
$x^2+15x+36=0$

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

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

$N_1*N_2 = a*c = 1*36 =36$
AND
$N_1 +N_2 = b = 15$
After trying out a few numbers we get $N_1 = 12$ and $N_2 =3$
$12*3 = 36$ , and $12+3=15$

$x^2+15x+36=x^2+12x +3x+36$

$=x(x+12) +3(x+12)$

$=(x+3)(x+12) =0$

Now we equate the factors to zero

$x+3=0, color(blue)(x=-3$
$x+12=0, color(blue)(x=-12$

How do you solve x^2+ 15x= -36x^2+ 15x= -36 by factoring?