How do you solve $x^2 + 2x - 15 = 0$ by factoring?

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Answer 1 · 2015-08-16T17:13:23

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

$color(blue)(x=-5$

$x^2+2x−15=0$

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:

$N_1*N_2 = a*c = 1*-15 = -15$
AND
$N_1 +N_2 = b = 2$

After trying out a few numbers we get $N_1 = 5$ and $N_2 =-3$
$5*-3 = -15$ , and $5+(-3)= 2$

$x^2+2x−15=x^2+5x-3x−15$

$x(x+5) -3(x+5)=0$

$(x-3)(x+5) =0$

Now we equate the factors to zero to find the solutions:
$x-3 =0, color(blue)(x=3$

$x+5 =0, color(blue)(x=-5$

How do you solve x^2 + 2x - 15 = 0x^2 + 2x - 15 = 0 by factoring?