Question

How do you solve `x^2+2x-6=0` by completing the square?

Answer 1

`x=-1+-sqrt7`

Explanation:

`x^2+2x-6=0`

Move the constant to the right side by adding 6 to both sides.

`x^2+color(magenta)2xcolor(white)(aaaaaa)=6`

Divide the coefficient `color(magenta)2` of the middle term `color(magenta)(2)x` by `2`:

`color(magenta)2/2 =color(blue)1`

Square the `color(blue)1` and add the result to both sides.

`color(blue)1^2=color(red)1`

`x^2+ 2x +color(red)1=6+color(red)1`

Factor the left side and sum the right side. Notice the `color(blue)1` in the factored form is the same `color(blue)1` you obtained by dividing the coefficient of the middle term by `2`

`(x+color(blue)1)(x+color(blue)1)=7`

Express the left side as the square of the binomial.

`(x+color(blue)1)^2=7`

Square root both sides.

`sqrt((x+1)^2)=sqrt7`

`x+1=+-sqrt7`

Subtract 1 from each side.

`x=-1+-sqrt7`