SOLUTION: Solve using quadratic formula y= 5x^2-8x-2 x= 8± sqrt ( 104 ) ----------- 10 x= 8 ± sqrt (4*26) ----------- --- 10 x= 8± 2 sqrt (26) ----------- -- 10

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Question 887003: Solve using quadratic formula
y= 5x^2-8x-2
x= 8± sqrt ( 104 )
------------
10
x= 8 ± sqrt (4*26)
---------------
10
x= 8± 2 sqrt (26)
--------------
10

x= 4± sqrt (26 )
------------
5
That is what I tried. Can you please correct me if something is wrong with my answer.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-8x%2B-2+=+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=%28-8%29%5E2-4%2A5%2A-2=104.

Discriminant d=104 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+104+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+104+%29%29%2F2%5C5+=+1.81980390271856
x%5B2%5D+=+%28-%28-8%29-sqrt%28+104+%29%29%2F2%5C5+=+-0.219803902718557

Quadratic expression 5x%5E2%2B-8x%2B-2 can be factored:
5x%5E2%2B-8x%2B-2+=+5%28x-1.81980390271856%29%2A%28x--0.219803902718557%29
Again, the answer is: 1.81980390271856, -0.219803902718557. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-8%2Ax%2B-2+%29

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 5%2Ax%5E2-8%2Ax-2=0 ( notice a=5, b=-8, and c=-2)





x+=+%28--8+%2B-+sqrt%28+%28-8%29%5E2-4%2A5%2A-2+%29%29%2F%282%2A5%29 Plug in a=5, b=-8, and c=-2




x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%2A5%2A-2+%29%29%2F%282%2A5%29 Negate -8 to get 8




x+=+%288+%2B-+sqrt%28+64-4%2A5%2A-2+%29%29%2F%282%2A5%29 Square -8 to get 64 (note: remember when you square -8, you must square the negative as well. This is because %28-8%29%5E2=-8%2A-8=64.)




x+=+%288+%2B-+sqrt%28+64%2B40+%29%29%2F%282%2A5%29 Multiply -4%2A-2%2A5 to get 40




x+=+%288+%2B-+sqrt%28+104+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)




x+=+%288+%2B-+2%2Asqrt%2826%29%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%288+%2B-+2%2Asqrt%2826%29%29%2F10 Multiply 2 and 5 to get 10


So now the expression breaks down into two parts


x+=+%288+%2B+2%2Asqrt%2826%29%29%2F10 or x+=+%288+-+2%2Asqrt%2826%29%29%2F10



Now break up the fraction



x=%2B8%2F10%2B2%2Asqrt%2826%29%2F10 or x=%2B8%2F10-2%2Asqrt%2826%29%2F10



Simplify



x=4%2F5%2Bsqrt%2826%29%2F5 or x=4%2F5-sqrt%2826%29%2F5



So the solutions are:

x=4%2F5%2Bsqrt%2826%29%2F5 or x=4%2F5-sqrt%2826%29%2F5