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

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Answer 1 · 2016-05-20T11:51:33

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

$x^2 + x - 20 = 0$

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

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

$N_1*N_2 = a*c = 1* (-20) = -20$

AND

$N_1 +N_2 = b = 1$

After trying out a few numbers we get $N_1 = -4$ and $N_2 =5$
$(-4)*5 = -20$ , and $5+(-4)= 1$

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

$= x(x+5) - 4(x + 5)$

$(x+5)$ 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:

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