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

1 Answer
Jul 2, 2017

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}