Question

How do you solve the quadratic equation by completing the square: `x^2 + 4x = 21`?

Answer 1

`x_(1,2) = -2 +- 5`

Explanation:

To solve this quadratic by completing the square, you need to use the coefficient of the `x`-term to help you find a number that when added to both sides of the equation will allow you to write the left side as the square of a binomial.

More specifically, you need to divide the coefficient of the `x`-term by `2`, the nsquare the result

`(4/2)^2 = 2^2 = 4`

Add this term to both sides of the equation to get

`x^2 + 4x + 4 = 21 + 4`

Now, the left side of the equaation can be written as

`x^2 + 4x + 4 = x^2 + 2 * (2) * x + (2)^2 = (x+2)^2`

This means that you now have

`(x+2)^2 = 25`

Take the square root of both sides

`sqrt((x+2)^2) = sqrt(25)`

`x+2 = +- 5`

`x = -2 +- 5 = {(x_1 = -2-5 = -7), (x_2 = -2 + 5 = 3) :}`