Question

How do you solve `x^2 - 3x = 40`?

Answer 1

`x=8,-5`

Explanation:

`color(blue)(x^2-3x=40`

Subtract `40` both sides

We get:

`color(red)(x^2-3x-40=0`

You can solve this both by Factoring and using the Quadratic formula:

`1)` First we can solve it by factoring:

`color(red)(x^2-3x-40=0`

Factor `x^2-3x-40`

We get

`rarr(x-8)(x+5)=0`

If you solve it you get

`rArrcolor(green)(x=8,-5`

`2)` Quadratic formula

`color(red)(x^2-3x-40=0`

This is a Quadratic equation (in form `ax^2+bx+c=0`)

So use Quadratic formula:

`color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)`

In this case `a=1,b=-3,c=-40`

Substitute the values into the equation:

`rarrx=(-(-3)+-sqrt(-3^2-4(1)(-40)))/(2(1))`

`rarrx=(3+-sqrt(9-(-160)))/(2)`

`rarrx=(3+-sqrt(9+160))/(2)`

`rarrx=(3+-sqrt(169))/(2)`

`rArrx=color(indigo)(3+-13)/2`

Now we have two solutions:

`x=color(orange)((3+13)/2),color(violet)((3-13)/2`

Solve for the first and then into the second:

`rarrx=color(orange)((3+13)/2`

`rArrcolor(green)(x=16/2=8`

For the second

`rarrcolor(violet)(x=(3-13)/2`

`rArrcolor(green)(x=-10/2=-5`