# How do you solve the equation -x^2 + 14x - 49 = 0 by graphing the related function?

Jun 25, 2018

$x = 7$

#### Explanation:

$- {x}^{2} + 14 x - 49 = 0$
${x}^{2} - 14 x + 49 = 0$
${\left(x - 7\right)}^{2} = 0$

This is a $y = {x}^{2}$ parabola that has been shifted to the right by 7 units.

graph{x^2 [-10, 10, -5, 5]}
Above is $y = {x}^{2}$

graph{(x-7)^2 [-10, 10, -5, 5]}
Above is $y = {\left(x - 7\right)}^{2}$

Hence, solving for ${\left(x - 7\right)}^{2} = 0$, the only possible answer is $x = 7$