Question

How do you solve the quadratic equation by completing the square: `x^2+6x=7`?

Answer 1

`x_(1,2) = -3 +- 4`

Explanation:

In order to solve this quadratic equation by completing the square, you need to write the left side of the equation as the square of a binomial.

To do that, you need to add a term to both sides of the equaion. More specifically, you need to divide the coefficient of `x`-term by 2 and square the result.

`6/2 = 3`, then `3^2 = 9`

Add `9` to both sides of the equation to get

`x^2 + 6x + 9 = 7 + 9`

The left side of the equation can now be written as

`x^2 + 6x + 9 = x^2 + 2 * (3) * x + (3^2)`

`x^2 + 6x + 9 = (x + 3)^2`

This will get you

`(x+3)^2 = 16`

Take the square root from both sides of the equation

`sqrt((x+3)^2) = sqrt(16)`

`x+3 = +- 4 => x_(1,2) = -3 +- 4 = {(x_1 = -3-4 = color(green)(-7)), (x_2 = -3 + 4 = color(green)(1)) :}`