How do you solve $x^2 + 8x = 7$ by completing the square?

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Answer 1 · 2016-05-09T22:12:46

$x = -4+-sqrt(23)$

If we add $16$ to both sides then the left hand side of the equation becomes a perfect square:

$x^2+8x+16 = 23$

That is:

$(x+4)^2 = 23$

So $x+4$ is a square root of $23$ .

It could be the positive or negative one:

$x+4 = +-sqrt(23)$

Subtract $4$ from both sides to find:

$x = -4+-sqrt(23)$

How do you solve x^2 + 8x = 7x^2 + 8x = 7 by completing the square?