SOLUTION: 12x^2 + 12x -9= 0 answer: x= -3/2 or 1/2 how did my text book get this answer i tought there was going to be a 4 involved because 4 .3 is 12

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: 12x^2 + 12x -9= 0 answer: x= -3/2 or 1/2 how did my text book get this answer i tought there was going to be a 4 involved because 4 .3 is 12      Log On


   

Question 183541: 12x^2 + 12x -9= 0
answer: x= -3/2 or 1/2


how did my text book get this answer i tought there was going to be a 4 involved because 4 .3 is 12
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
12x^2 + 12x -9= 0
answer: x= -3/2 or 1/2
----------------
Divide by 3
4x%5E2+%2B+4x+-+3+=+0
Factor it
(2x+3)*(2x-1) = 0
Either 2x+3 = 0, or 2x-1 = 0
2x+3 = 0
x = -3/2
-----------
2x-1 = 0
x = 1/2
-----------
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-3+=+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-3=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+64+%29%29%2F2%5C4+=+0.5
x%5B2%5D+=+%28-%284%29-sqrt%28+64+%29%29%2F2%5C4+=+-1.5

Quadratic expression 4x%5E2%2B4x%2B-3 can be factored:
4x%5E2%2B4x%2B-3+=+%28x-0.5%29%2A%28x--1.5%29
Again, the answer is: 0.5, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B4%2Ax%2B-3+%29

NOTE: The solver gets the right answers, but the factors are not right.