Question

Solve the equation x^2+6x= -11/4

Answer 1

Explanation:

First, move the -11/4 to the other side, so the expression can equal 0.

`x^2+6x+11/4=0`

To make the equation easier to work with, multiply both sides by 4, cancelling out the fraction.

`4x^2+24x+11=0`

There are many ways to solve a quadratic equation (factoring, quadratic formula, completing the square).

Solving this equation by factoring is the easiest. Factoring with a leading coefficient greater than one can be difficult and there are many ways to accomplish it. The way I'm going to do it is to first find the factors of
`4x^2` and then the factors of 11. And then multiply across, add the middle terms (derived from multiplying) and try to make it equal 24x.

`4x^2`: 24x 11:

2x 22x 11

2x 2x 1

24x (works)

I'll then take the factors diagonal. (2x+1)(2x+11)=0

So
`x=-(1)/(2), -(11)/(2)`