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How do you complete the square to solve $x^{2} + 6 x = - 8$ $x^2 + 6x = -8$ ?

1 Answer

Jun 3, 2015

Given $x^{2} + 6 x = - 8$ $x^2+6x = -8$

If $x^{2} + 6 x$ $x^2+6x$ are the first two terms of a squared binomial of the form:
$XXXX$ $color(white)("XXXX")$ ${(x + a)}^{2} = x^{2} + 2 a x + a^{2}$ $(x+a)^2 = x^2+2ax+a^2$
then
$XXXX$ $color(white)("XXXX")$ $a = 3$ $a=3$

$x^{2} + 6 x + 9 = - 8 + 9$ $x^2 +6x +9 = -8 +9$

${(x + 3)}^{2} = 1$ $(x+3)^2 = 1$

$x + 3 = \pm 1$ $x+3 = +-1$

$x = - 2$ $x= -2$ or $x = - 4$ $x=-4$

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