Question

Solve the equation by completing the squares.
x^2−10x = 11
x= __ and __

Answer 1

x = 11 and x = -1

Explanation:

We have x^2−10x = 11 and want to make a perfect square out of x^2−10x.

To do this, take half of the coefficient of x, square this half, and then add and then subtract the square immediately following x^2−10x:

Half of -10 is -5, and the square of -5 is 25.

x^2−10x = 11 becomes x^2 - 10x + 25 - 25 = 11

Rewrite x^2−10x + 25 as the square of a binomial: (x - 5)^2.

Then we have (x - 5)^2 - 25 = 11. Solve this for x -5:

(x - 5)^2 = 36. Taking the square root of both sides, we get

x - 5 = ±6

Then x = 11 and x = -1