# How do you solve x^2 + 5x - 6 = 0 by factoring?

Sep 29, 2015

The solutions are

color(blue)(x=1

color(blue)(x=-6

#### Explanation:

x^2+5x−6=0

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

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 6 = - 6$

AND

${N}_{1} + {N}_{2} = b = 5$

After trying out a few numbers we get ${N}_{1} = 6$ and ${N}_{2} = - 1$

$6 \cdot - 1 = - 6$, and $6 + \left(- 1\right) = 5$

x^2+5x−6=x^2+6x-1x−6

$= x \left(x + 6\right) - 1 \left(x + 6\right)$

$= \left(x - 1\right) \left(x + 6\right)$

Now we equate the factors to zero:

x-1=0 , color(blue)(x=1

x+6=0 , color(blue)(x=-6

Sep 29, 2015

Solve y = x^2 + 5x - 6 = 0

Ans: 1 and (-6)

#### Explanation:

Since (a + b + c = 0), use the Shortcut. The 2 real roots are: 1 and (c/a) = -6.