Question

How do you solve `4x^2+40x+280=0` by completing the square?

Answer 1

You can't, unless you want to have complex numbers. If you want complex numbers, then the answer would be `x=-5\pm3i\sqrt{5}`

Explanation:

You can simplify the quadratic to make completing the square easier:
`4x^2+40x+280=0`
`x^2+10x+70=0`

Completing the square:
`x^2+10x+70=0`
`x^2+10x=-70`
`x^2+10x+(10/2)^2=-70+(10/2)^2`
`x^2+10x+25=-70+25`
`(x+5)^2=-45`

We cannot continue here, since there is no way for the above equation to be true.

However, if you want to have complex numbers, we can continue:
`x+5=\pm\sqrt{-45}`
`x+5=\pmi\sqrt{45}`
`x+5=\pm3i\sqrt{5}`
`x=-5\pm3i\sqrt{5}`