SOLUTION: Hello. Can you please help me? I have to find the solutions of -8x^2 + 4x + 5= 0...I got to the point of -4+-*radical*176/-16....can you show me what to do next, please? th

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hello. Can you please help me? I have to find the solutions of -8x^2 + 4x + 5= 0...I got to the point of -4+-*radical*176/-16....can you show me what to do next, please? th      Log On


   

Question 378380: Hello. Can you please help me?
I have to find the solutions of -8x^2 + 4x + 5= 0...I got to the point of
-4+-*radical*176/-16....can you show me what to do next, please?
thank you!
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
-8x^2 + 4x + 5= 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -8x%5E2%2B4x%2B5+=+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%2A-8%2A5=176.

Discriminant d=176 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+176+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+176+%29%29%2F2%5C-8+=+-0.57915619758885
x%5B2%5D+=+%28-%284%29-sqrt%28+176+%29%29%2F2%5C-8+=+1.07915619758885

Quadratic expression -8x%5E2%2B4x%2B5 can be factored:
-8x%5E2%2B4x%2B5+=+%28x--0.57915619758885%29%2A%28x-1.07915619758885%29
Again, the answer is: -0.57915619758885, 1.07915619758885. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B4%2Ax%2B5+%29

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Just some minor simplification from where you were:
--------
x = (1 ± sqrt(11))/4

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the solutions of
-8x^2 + 4x + 5= 0
------------------
x = [-4 +- sqrt(16 -4*-8*5)]/(-16)
----
x = [-4 +- sqrt(176)]/(-16)
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x = [-4 +- 4sqrt(11)]/(-16
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x = [1+sqrt(11)]/4 or x = [1-sqrt(11]/4
=============================================
Cheers,
Stan H.