Question

How do you solve using the completing the square method `a^2+3a-40=0`?

Answer 1

`a=5`
`a=-8`

Explanation:

Given -

`a^2+3a-40=0`

Take the constant term to the right

`a^2+3a=40`

Divide the coefficient of `x` by 2. Square it and add the same to both sides

`a^2+3/2x+9/4=40+9/4`

`(a+3/2)^2=(160+9)/4=169/4`

`a+3/2=+-sqrt(169/4)=+-13/2`

`a=13/2-3/2=10/2=5`

`a=-13/2-3/2=-16/2=-8`