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# How do you factor and solve x^2+x-20=0 ?

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#### Explanation

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#### Explanation:

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16
May 20, 2016

The solutions are $x = 4 , x = - 5$

#### Explanation:

${x}^{2} + x - 20 = 0$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot \left(- 20\right) = - 20$

AND

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

After trying out a few numbers we get ${N}_{1} = - 4$ and ${N}_{2} = 5$
$\left(- 4\right) \cdot 5 = - 20$, and $5 + \left(- 4\right) = 1$

${x}^{2} + x - 20 = {x}^{2} + 5 x - 4 x - 20$

$= x \left(x + 5\right) - 4 \left(x + 5\right)$

$\left(x + 5\right)$ is a common factor to each of the terms

=color(green)((x-4)(x+5)

We equate both factors to zero and obtain the solutions:

• $x - 4 = 0 , x = 4$
• $x + 5 = 0 , x = - 5$
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