Question

How do you solve the quadratic equation by completing the square: `x^2 + 24 = - 10x`?

Answer 1

I found:
`x_1=-4`
`x_2=-6`

Explanation:

Try this:
`x^2+10x=-24`
add and subtract `25`:
`x^2+10xcolor(red)(+25-25)=-24`
rearrange:
`x^2+10x+25=25-24`
`(x+5)^2=1`
square root both sides:
`x^2+5=+-sqrt(1)=+-1`
so you get two solutions:
`x_1=-5+1=-4`
`x_2=-5-1=-6`