Question

How do you solve `x^2+10x-1=0` using completing the square?

Answer 1

`x = -5+-sqrt(26)`

Explanation:

`x^2+10x-1 = 0`

simplify by moving the constant to the right side
`color(white)("XXXX")` `x^2+10x = 1`

complete the square
`color(white)("XXXX")` `x^2+10x+(10/2)^2 = 1 + (10/2)^2`

rewrite as a square and simplify the right side
`color(white)("XXXX")` `(x+5)^2 = 26`

take the square root of both sides
`color(white)("XXXX")` `x+5 = +-sqrt(26)`

subtract `5` from both sides to isolate `x`
`color(white)("XXXX")` `x = -5+-sqrt(26)`