Question

Solve x2 − 8x + 5 = 0 using the completing-the-square method.

Answer 1

$x^2 - 8x + 5 = 0\\ x^2-8x+16-11=0\\ (x-4)^2=11\\ x-4=\sqrt{11} \vee x-4=-\sqrt{11}\\ x=4+\sqrt{11} \vee x=4-\sqrt{11}$

Answer 2

First, let's move the 5 to the other side by subtracting both sides by 5. That leaves us with:

x^2 - 8x = -5

The constant on the left side to make a binomial square should be (8/2)^2 = 16. Add 16 to both sides and you get: x^2 - 8x + 16 = 11

(x - 4)^2 = 11

Square root both sides:

(x - 4) = +/- sqrt (11)

Add 4 to both sides:

x = +/- sqrt (11) + 4

The 4 should be outside the square root.