How do you solve x^2+14x=-49?

Apr 6, 2016

$x = - 7$

Explanation:

$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + 14 x = - 49$
is equivalent to
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + 14 x + 49 = 0$
which can be factored as
$\textcolor{w h i t e}{\text{XXX}} \left(x + 7\right) \left(x + 7\right) = 0$
which can only be true if
$\textcolor{w h i t e}{\text{XXX}} \left(x + 7\right) = 0$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = - 7$