SOLUTION: I have spent close to two hours trying to work out the following: 12x(squared) + 13x = 4 I have followed the rules and still am unable to solve it correctly. I've come up wi

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I have spent close to two hours trying to work out the following: 12x(squared) + 13x = 4 I have followed the rules and still am unable to solve it correctly. I've come up wi      Log On


   

Question 985359: I have spent close to two hours trying to work out the following:
12x(squared) + 13x = 4
I have followed the rules and still am unable to solve it correctly. I've come up with 5 incorrect solutions. I am clearly missing something.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
12x%5E2+%2B+13x+=+4
12x%5E2+%2B+13x+-4+=+0
Use the quadratic equation to solve
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B13x%2B-4+=+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=%2813%29%5E2-4%2A12%2A-4=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-13%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+361+%29%29%2F2%5C12+=+0.25
x%5B2%5D+=+%28-%2813%29-sqrt%28+361+%29%29%2F2%5C12+=+-1.33333333333333

Quadratic expression 12x%5E2%2B13x%2B-4 can be factored:
12x%5E2%2B13x%2B-4+=+12%28x-0.25%29%2A%28x--1.33333333333333%29
Again, the answer is: 0.25, -1.33333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B13%2Ax%2B-4+%29