SOLUTION: 30=1/2×3(x+1)(2x-1)

Algebra ->  Equations -> SOLUTION: 30=1/2×3(x+1)(2x-1)      Log On


   

Question 972437: 30=1/2×3(x+1)(2x-1)
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
30=%281%2F2%29%2A3%28x%2B1%29%282x-1%29 Multiply each side by 2/3.
20=2x%5E2%2Bx-1
0=2x%5E2%2Bx-21
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B1x%2B-21+=+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=%281%29%5E2-4%2A2%2A-21=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+169+%29%29%2F2%5C2+=+3
x%5B2%5D+=+%28-%281%29-sqrt%28+169+%29%29%2F2%5C2+=+-3.5

Quadratic expression 2x%5E2%2B1x%2B-21 can be factored:
2x%5E2%2B1x%2B-21+=+2%28x-3%29%2A%28x--3.5%29
Again, the answer is: 3, -3.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B1%2Ax%2B-21+%29

ANSWER: x=3 or x=-3.5