SOLUTION: How do you solve the following equations? Thanks! -2x^2 – 2x +24 = 0 and 4x^2 + 11x = 3

Algebra ->  Equations -> SOLUTION: How do you solve the following equations? Thanks! -2x^2 – 2x +24 = 0 and 4x^2 + 11x = 3      Log On


   

Question 220065: How do you solve the following equations? Thanks!
-2x^2 – 2x +24 = 0
and
4x^2 + 11x = 3
Answer by likaaka(51) About Me  (Show Source):
You can put this solution on YOUR website!
Basically it depends on whether you must solve using the quadratic equation or by factoring. Below it is solved with quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B-2x%2B24+=+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=%28-2%29%5E2-4%2A-2%2A24=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+196+%29%29%2F2%5C-2+=+-4
x%5B2%5D+=+%28-%28-2%29-sqrt%28+196+%29%29%2F2%5C-2+=+3

Quadratic expression -2x%5E2%2B-2x%2B24 can be factored:
-2x%5E2%2B-2x%2B24+=+-2%28x--4%29%2A%28x-3%29
Again, the answer is: -4, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B-2%2Ax%2B24+%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B11x%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=%2811%29%5E2-4%2A4%2A-3=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-11%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2811%29%2Bsqrt%28+169+%29%29%2F2%5C4+=+0.25
x%5B2%5D+=+%28-%2811%29-sqrt%28+169+%29%29%2F2%5C4+=+-3

Quadratic expression 4x%5E2%2B11x%2B-3 can be factored:
4x%5E2%2B11x%2B-3+=+4%28x-0.25%29%2A%28x--3%29
Again, the answer is: 0.25, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B11%2Ax%2B-3+%29