SOLUTION: Solve the equations using the quadratic formula. Round to the nearest hundredth when necessary. 2x2 + 3x - 5 = 0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve the equations using the quadratic formula. Round to the nearest hundredth when necessary. 2x2 + 3x - 5 = 0      Log On


   

Question 975625: Solve the equations using the quadratic formula. Round to the nearest hundredth when necessary.
2x2 + 3x - 5 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!

2x2 + 3x - 5 = 0
Use ^ (Shift 6) for exponents.
2x^2 + 3x - 5 = 0
------------------------------
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B3x%2B-5+=+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=%283%29%5E2-4%2A2%2A-5=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+49+%29%29%2F2%5C2+=+1
x%5B2%5D+=+%28-%283%29-sqrt%28+49+%29%29%2F2%5C2+=+-2.5

Quadratic expression 2x%5E2%2B3x%2B-5 can be factored:
2x%5E2%2B3x%2B-5+=+%28x-1%29%2A%28x--2.5%29
Again, the answer is: 1, -2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B3%2Ax%2B-5+%29