Question

Which of the following are solutions to the equation below? Check all that apply. X^2 - 8x + 16 = 5

Answer 1

Given equation is

$\begin{gathered} x^2-8x+16=5 \\ x^2-8x+16-5=0 \\ x^2-8x+11=0 \end{gathered}$

The quadratic formula for the quadratic equation

$ax^2+bx+c=0$

is

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

Here, a=1,b=-8,c=11.

$\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(11)}}{2(1)} \\ =\frac{8\pm\sqrt[]{64-44}}{2} \\ =\frac{8\pm\sqrt[]{20}}{2} \\ =\frac{8\pm\sqrt[]{5\cdot4}}{2} \\ =\frac{8\pm2\sqrt[]{5}}{2} \\ =\frac{8}{2}\pm\frac{2\sqrt[]{5}}{2} \\ =4\pm\sqrt[]{5} \end{gathered}$

So, the solutions are

$\sqrt[]{5}+4,-\sqrt[]{5}+4$

So, the correct options are C and E.