SOLUTION: I need your help on this quadratic formula question. You have to solve it using the formula. the problem is 10x squared-5x+5=-25x it has to be set equal to zero beforing solving. I

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I need your help on this quadratic formula question. You have to solve it using the formula. the problem is 10x squared-5x+5=-25x it has to be set equal to zero beforing solving. I      Log On


   

Question 433700: I need your help on this quadratic formula question. You have to solve it using the formula. the problem is 10x squared-5x+5=-25x it has to be set equal to zero beforing solving. I am getting a little stuck half way through, i would really appreciate your help.
Found 2 solutions by psbhowmick, Alan3354:
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
10x%5E2-5x%2B5=-25x
10x%5E2%2B20x%2B5=0
2x%5E2%2B10x%2B1=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B10x%2B1+=+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=%2810%29%5E2-4%2A2%2A1=92.

Discriminant d=92 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+92+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+92+%29%29%2F2%5C2+=+-0.10208423834364
x%5B2%5D+=+%28-%2810%29-sqrt%28+92+%29%29%2F2%5C2+=+-4.89791576165636

Quadratic expression 2x%5E2%2B10x%2B1 can be factored:
2x%5E2%2B10x%2B1+=+%28x--0.10208423834364%29%2A%28x--4.89791576165636%29
Again, the answer is: -0.10208423834364, -4.89791576165636. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B10%2Ax%2B1+%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
10x%5E2+-+5x+%2B+5+=+-25x
10x%5E2+%2B+20x+%2B+5+=+0
2x%5E2+%2B+4x+%2B+1+=+0 *** It's not required to reduce it, but it can help in some cases.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B1+=+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=%284%29%5E2-4%2A2%2A1=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+8+%29%29%2F2%5C2+=+-0.292893218813452
x%5B2%5D+=+%28-%284%29-sqrt%28+8+%29%29%2F2%5C2+=+-1.70710678118655

Quadratic expression 2x%5E2%2B4x%2B1 can be factored:
2x%5E2%2B4x%2B1+=+%28x--0.292893218813452%29%2A%28x--1.70710678118655%29
Again, the answer is: -0.292893218813452, -1.70710678118655. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B1+%29

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x+=+-1+-+sqrt%282%29%2F2
x+=+-1+%2B+sqrt%282%29%2F2