SOLUTION: 14. Solve each equation with the quadratic formula 9v^2 + 10v = 18

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Question 540900: 14. Solve each equation with the quadratic formula

9v^2 + 10v = 18

Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
9v%5E2+%2B+10v+=+18
9v%5E2+%2B+10v+-+18+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation av%5E2%2Bbv%2Bc=0 (in our case 9v%5E2%2B10v%2B-18+=+0) has the following solutons:

v%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=%2810%29%5E2-4%2A9%2A-18=748.

Discriminant d=748 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+748+%29%29%2F2%5Ca.

v%5B1%5D+=+%28-%2810%29%2Bsqrt%28+748+%29%29%2F2%5C9+=+0.963866036797483
v%5B2%5D+=+%28-%2810%29-sqrt%28+748+%29%29%2F2%5C9+=+-2.07497714790859

Quadratic expression 9v%5E2%2B10v%2B-18 can be factored:
9v%5E2%2B10v%2B-18+=+9%28v-0.963866036797483%29%2A%28v--2.07497714790859%29
Again, the answer is: 0.963866036797483, -2.07497714790859. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B10%2Ax%2B-18+%29