SOLUTION: 1) 2x^2-6x+1=0 2) 4x^2-6x-1=0

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Question 82198: 1) 2x^2-6x+1=0

2) 4x^2-6x-1=0
Found 2 solutions by jim_thompson5910, checkley75:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-6x%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=%28-6%29%5E2-4%2A2%2A1=28.

Discriminant d=28 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+28+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+28+%29%29%2F2%5C2+=+2.8228756555323
x%5B2%5D+=+%28-%28-6%29-sqrt%28+28+%29%29%2F2%5C2+=+0.177124344467705

Quadratic expression 2x%5E2%2B-6x%2B1 can be factored:
2x%5E2%2B-6x%2B1+=+2%28x-2.8228756555323%29%2A%28x-0.177124344467705%29
Again, the answer is: 2.8228756555323, 0.177124344467705. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-6%2Ax%2B1+%29


2)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-6x%2B-1+=+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=%28-6%29%5E2-4%2A4%2A-1=52.

Discriminant d=52 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+52+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+52+%29%29%2F2%5C4+=+1.651387818866
x%5B2%5D+=+%28-%28-6%29-sqrt%28+52+%29%29%2F2%5C4+=+-0.151387818865997

Quadratic expression 4x%5E2%2B-6x%2B-1 can be factored:
4x%5E2%2B-6x%2B-1+=+4%28x-1.651387818866%29%2A%28x--0.151387818865997%29
Again, the answer is: 1.651387818866, -0.151387818865997. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-6%2Ax%2B-1+%29

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2-6x+1=0
using the quadratic equation we get:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=(6+-sqrt[-6^2-4*2*1[)/2*2
x=(6+-sqrt36-8])/4
x=(6+-sqrt28)/4
x=(6+-5.29)/4
x=(6+5.29)/4
x=11.29/4
x=2.8225 answer.
x=(6-5.29)/4
x=.71/4
x=.1775 answer.
--------------------------------------
4x^2-6x+1=0
x=(6+-sqrt[-6^2-4*4*1])/2*4
x=(6+-sqrt[36-16])/8
x=(6+-sqrt20)/8
x=(6+-4.47)/8
x=(6+4.47)/8
x=10.47/8
x=1.309 answer.
x=(6-4.47)/8
x=1.53/8
x=.19 answer.