How do you solve the quadratic equation by completing the square: x^2-12x+20=0?

Jul 22, 2015

I found:
${x}_{1} = 10$
${x}_{2} = 2$

Explanation:

${x}^{2} - 12 x = - 20$
add and subtract $36$;
${x}^{2} - 12 x \textcolor{red}{+ 36 - 36} = - 20$
${x}^{2} - 12 x + 36 = - 20 + 36$
$\textcolor{b l u e}{{\left(x - 6\right)}^{2} = 16}$
$x - 6 = \pm \sqrt{16} = \pm 4$
${x}_{1} = 6 + 4 = 10$
${x}_{2} = 6 - 4 = 2$