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

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

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Answer 1 · 2015-07-17T17:27:01

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:
$x_1=-5+1=-4$
$x_2=-5-1=-6$

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

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Explanation:

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