Question

Find the zeros of the following equation by completing the square.
x^2+8x-2=0

Answer 1

x = -4 + 3√2 and x = -4 - 3√2

Explanation:

Complete the square of x^2+8x-2=0:

Between 8x and -2, write in 4^2 - 4^2, so that we now have:

x^2 + 8x + 16 - 16 - 2 = 0, or by writing x^2 + 8x + 16 as the square of a binomial, (x + 4)^2 = 18

Taking the square root of both sides, we get:

x + 4 = √18 = ±√9√2, or ±3√2

Then x = -4 + 3√2 and x = -4 - 3√2