Question

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

Answer 1

`x=4,-5`

Explanation:

`color(blue)(x^2+x-20=0`

First, Factor the equation:

`rarrx^2+5x-4x-20=0`

`rarrx(x+5)-4(x+5)=0`

`color(purple)(rarr(x-4)(x+5)=0`

`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

Next, set both equations equal to zero, and solve.

`rarrx-4=0`

Add four to each side, and solve:

`rarrxcancel(-4+4)=0+4`

`color(green)(rArrx=4`

`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

`rarrx+5=0`

Subtract `5` from each side, and solve:

`rarrxcancel(+5-5)=0-5`

`color(green)(rArrx=-5`

`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

`:.color(indigo)( ul bar |x=4, -5|`