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How do you solve $x^{2} + 2 a x = b^{2} - a^{2}$ $x^2+2ax = b^2-a^2$ by factoring?

1 Answer

Aug 11, 2015

$x = - a - b$ $x=-a-b$
or
$x = - a + b$ $x=-a+b$

Explanation:

Given $x^{2} + 2 a x = b^{2} - a^{2}$ $x^2+2ax = b^2 -a^2$

$\Rightarrow$ $rArr$ $XXXX$ $color(white)("XXXX")$ x^2+2ax+a^2 = b^2#

Factoring the left side:
$\Rightarrow$ $rArr$ $XXXX$ $color(white)("XXXX")$ ${(x + a)}^{2} = b^{2}$ $(x+a)^2 = b^2$

Taking the square root:
$\Rightarrow$ $rArr$ $XXXX$ $color(white)("XXXX")$ $x + a = \pm b$ $x+a = +-b$

Subtracting $a$ $a$ from both sides:
$\Rightarrow$ $rArr$ $XXXX$ $color(white)("XXXX")$ $x = - a \pm b$ $x = -a+-b$

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