SOLUTION: Solve using the quadratic formula: 4x squared+4x=15 I have tried to plug this into the formula, but I don't know if I have to do anything special to the 4x squared, since the

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve using the quadratic formula: 4x squared+4x=15 I have tried to plug this into the formula, but I don't know if I have to do anything special to the 4x squared, since the      Log On


   

Question 196701This question is from textbook Prentice Hall Algebra 1
: Solve using the quadratic formula:
4x squared+4x=15
I have tried to plug this into the formula, but I don't know if I have to do anything special to the 4x squared, since there is a 4 in there.
Thanks in advance!! :) This question is from textbook Prentice Hall Algebra 1

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula:
4x squared+4x=15
--------
4x%5E2+%2B+4x+-+15+=+0
(2x-3)*(2x+5) = 0
x = 3/2
x = -5/2
--------------
Using quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B4x%2B-15+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A4%2A-15=256.

Discriminant d=256 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+256+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+256+%29%29%2F2%5C4+=+1.5
x%5B2%5D+=+%28-%284%29-sqrt%28+256+%29%29%2F2%5C4+=+-2.5

Quadratic expression 4x%5E2%2B4x%2B-15 can be factored:
4x%5E2%2B4x%2B-15+=+%28x-1.5%29%2A%28x--2.5%29
Again, the answer is: 1.5, -2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B4%2Ax%2B-15+%29