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

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Answer 1 · 2015-03-30T12:37:01

Since $(x+a)^2 = x^2+2ax + a^2$

If $x^2 +8x$ are the first 2 terms of a squared expression
the third term must be $(8/2)^2 = 16$

Add $16$ to each side of the equation, giving
$x^2+8x+16 = 23$
which is the same as
$(x+4)^2 = 23$

Taking the square root of both sides
$x+4 = +-sqrt(23)$

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

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