Question

How do you solve using the completing the square method `x^2 + 4x = 6`?

Answer 1

`x=-2+-sqrt(10)`

Explanation:

When wanting to complete the square for a quadratic in the form

`ax^2+bx=c`, we add `(b/2)^2` to each side and factor the left side. To solve, we can take the root of both sides, accounting for positive and negative answers on the right side.

In this case, `b=4, (b/2)^2=(4/2)^2=2^2=4`, so we add `4` to each side.

`x^4+4x+4=6+4`

Factoring `x^4+4x+4` yields `(x+2)^2`

`(x+2)^2=10`

So, take the root of both sides, account for positive and negative:

`sqrt((x+2)^2)=+-sqrt(10)`

The root of a squared term is just that term:

`x+2=+-sqrt(10)`

`x=-2+-sqrt(10)`