Answer:
Step-by-step explanation:
First, move the -11/4 to the other side, so the expression can equal 0.
[tex]x^2+6x+11/4=0[/tex]
To make the equation easier to work with, multiply both sides by 4, cancelling out the fraction.
[tex]4x^2+24x+11=0[/tex]
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 [tex]4x^2[/tex] and then the factors of 11. And then multiply across, add the middle terms (derived from multiplying) and try to make it equal 24x.
[tex]4x^2[/tex]: 24x 11:
2x 22x 11
2x 2x 1
24x (works)
I'll then take the factors diagonal. (2x+1)(2x+11)=0
So [tex]x=-\frac{1}{2}, -\frac{11}{2}[/tex]
