SOLUTION: I am having a problem with this problem, can you please help clarify. Thank you so much. Use quadratic formula to solve: 5x^2+5x+1= 0 Thank you in advance for your expert

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am having a problem with this problem, can you please help clarify. Thank you so much. Use quadratic formula to solve: 5x^2+5x+1= 0 Thank you in advance for your expert      Log On


   

Question 114347: I am having a problem with this problem, can you please help clarify. Thank you so much.
Use quadratic formula to solve:
5x^2+5x+1= 0
Thank you in advance for your expertise.
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2%2B5x%2B1=+0

All you need to do is plug the coefficients into the quadratic formula and then do the arithmetic.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B5x%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=%285%29%5E2-4%2A5%2A1=5.

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

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+5+%29%29%2F2%5C5+=+-0.276393202250021
x%5B2%5D+=+%28-%285%29-sqrt%28+5+%29%29%2F2%5C5+=+-0.723606797749979

Quadratic expression 5x%5E2%2B5x%2B1 can be factored:
5x%5E2%2B5x%2B1+=+5%28x--0.276393202250021%29%2A%28x--0.723606797749979%29
Again, the answer is: -0.276393202250021, -0.723606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B5%2Ax%2B1+%29



The plug in solver did the calculator math, but I would just leave the solution as:

%28-5%2Bsqrt%285%29%29%2F10 and %28-5-sqrt%285%29%29%2F10

since I expect your instructor wants the exact solution in this case.

I'll leave it as an exercise for you to plug each of these values for x back into the original equation to check them.

Hope this helps.
John

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

5x%5E2%2B5x%2B1=+0
x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29
x%5B1%2C2%5D=%28-5+%2B-+sqrt+%285%5E2+-4%2A5%2A1+%29%29+%2F+%282%2A5%29
x%5B1%2C2%5D=%28-5+%2B-+sqrt+%2825+-+20+%29%29+%2F+10
x%5B1%2C2%5D=%28-5+%2B-+sqrt+%285+%29%29+%2F+10
x%5B1%2C2%5D=%28-5+%2B-+2.24%29+%2F+10

x%5B1%5D=%28-5+%2B+2.24%29+%2F+10

x%5B1%5D=-+2.76+%2F+10
x%5B1%5D=+-+0.276+

x%5B1%2C2%5D=%28-5+-+2.24%29+%2F+10
x%5B1%2C2%5D=%28+-+7.24%29+%2F+10
x%5B1%2C2%5D=%28+-+0.724%29+

Check:
5x%5E2%2B5x%2B1=+0…..plug in x
5%28-+0.276+%29%5E2%2B5%28-+0.276+%29%2B1=+0
5%280.076176%29%2B5%28-+0.276+%29%2B1=+0
0.38+-+1.38+%2B+1=+0
1.38+-+1.38+=+0
0+=+0

5x%5E2%2B5x%2B1=+0…..plug in x

5%28-+0.724%29%5E2%2B5%28-+0.724%29%2B1=+0

5%280.524%29+-+3.62%2B1=+0
2.62-+3.62+%2B+1=+0
3.62-+3.62+=+0
0+=+0