Question

Question #3b81a

Answer 1

Alright, let's re-write the first problem.

`x^2+4x=10`

Okay, we have a quadratic equation. The purpose of "completing the square" is to add a constant to both sides of the equation so that we can turn the left side into some form of `(x+a)^2` , which is much easier to solve.

Let's go step by step.

First, take the half of the `x` coefficient.

`4/2=2`

Second, square it.

`2^2=4`

Third, add that result to both sides of the equation.

`x^2+4x+4=14`

Notice anything about the left side of the equation? It can be simplified into a form like `(x+a)^2` In this case,

`(x+2)^2=14`

which is much easier to solve than what we had originally.

`x+2 = +-sqrt 14`

`x = sqrt 14 - 2`

`x = -sqrt 14 - 2`

note the two answers.

I won't go over the other three questions because now that you know how to do complete the square, they should come really easily! Good luck!