SOLUTION: 25+15y+2y^2=228

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 25+15y+2y^2=228      Log On


   

Question 754329: 25+15y+2y^2=228
Answer by vidya pattar(14) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:
Here you have :
25 + 15y + 2y^2 = 228
now try to get rid of 228 from the right side.
25 - 228 +15y + 2y^2 =0
now combine the like terms :
-223 + 15y + 2y^2 = 0
now arange them in increasing order.
2y^2 +15y - 223 = 0
now to solve for x you have use the quadratic rquation:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B15x%2B-223+=+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=%2815%29%5E2-4%2A2%2A-223=2009.

Discriminant d=2009 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-15%2B-sqrt%28+2009+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2815%29%2Bsqrt%28+2009+%29%29%2F2%5C2+=+7.45546741550748
x%5B2%5D+=+%28-%2815%29-sqrt%28+2009+%29%29%2F2%5C2+=+-14.9554674155075

Quadratic expression 2x%5E2%2B15x%2B-223 can be factored:
2x%5E2%2B15x%2B-223+=+2%28x-7.45546741550748%29%2A%28x--14.9554674155075%29
Again, the answer is: 7.45546741550748, -14.9554674155075. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B15%2Ax%2B-223+%29

so here you get "
x = (-15 +/- sqrt ( 15^2 - 4(2)(-223)) )/ 2(2)
x = -15 +/- sqrt ( 2009)/4
hence we get after calculation x = 7.45 and x = - 14.955
Thanks & regards
Vidya pattar