# How do you solve by completing the square for x^2-7x+12=0?

May 27, 2015

$f \left(x\right) = {x}^{2} - 7 x + \frac{49}{4} - \frac{49}{4} + 12 = 0$

$f \left(x\right) = {\left(x - \frac{7}{2}\right)}^{2} - \frac{49}{4} + \frac{48}{4} = 0$

$\left(x - \frac{7}{2}\right) = \pm \frac{1}{2}$

$x = \frac{7}{2} \pm \frac{1}{2}$

$x = \frac{8}{2} = 4$
or
$x = \frac{6}{2} = 3$