Question

How do you solve `x^2+6x-1=0`?

Answer 1

Solve this equation by completing the square.

`x=sqrt10-3`

`x=-sqrt10-3`

Explanation:

Solve `x^2+6x-1=0`

We are going to create a perfect square trinomial on the left side of the equation. A perfect square trinomial has the form `a^2+2ab+b^2=(a+b)^2`. Then we can factor the perfect square trinomial and solve for `x`.

Add the constant term `(1)` to both sides of the equation.

`x^2+6x=1`

Divide the coefficient of the `x` term by `2`, square the result, and add it to both sides of the equation.

`6/2=3`; `3^2=9`

`x^2+6x+9=10`

We now have a perfect square trinomial on the left side which can be factored to `(x+3)^2`.

`(x+3)^2=10`

Take the square root of both sides.

`x+3=+-sqrt 10`

`x=+-sqrt10-3`

`x=sqrt10-3`

`x=-sqrt10-3`