Question

Conplete the square to solve the quadratic equation. x%2B%2012%20%3D%202x%20%2B%2020" id="TexFormula1" title="1 {x}^{2} - 6x + 12 = 2x + 20" alt="1 {x}^{2} - 6x + 12 = 2x + 20" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$\large\boxed{x=4\pm2\sqrt6}$

Step-by-step explanation:

$x^2-6x+12=2x+20\qquad\text{subtract}\ 2x\ \text{and}\ 12\ \text{from both sides}\\\\x^2-8x=8\\\\x^2-2(x)(4)=8\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\x^2-2(x)(4)+4^2=8+4^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-4)^2=24\iff x-4=\pm\sqrt{24}\\\\x-4=\pm\sqrt{4\cdot6}\\\\x-4=\pm\sqrt4\cdot\sqrt6\\\\x-4=\pm2\sqrt6\qquad\text{add 4 to both sides}\\\\x=4\pm2\sqrt6$