SOLUTION: Please help show me how to work this problem out..Thank you... solve equation using the quadratic formula 1/3x^2 + 2/9x - 1 = 0

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Question 169895: Please help show me how to work this problem out..Thank you...
solve equation using the quadratic formula
1/3x^2 + 2/9x - 1 = 0
Found 4 solutions by stanbon, Alan3354, Earlsdon, gonzo:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve equation using the quadratic formula
1/3x^2 + 2/9x - 1 = 0
Multiply thru by 9 to get rid of the fractions:
3x^2 + 2x - 9 = 0
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x = [-2 +- sqrt(4 - 4*3*-9)]/6
x = [-2 +- sqrt(112)]/6
x = [-2 +- 2sqrt(7)]/6
x = [-1 +- sqrt(7)]/3
===========================
Cheers,
Stan H.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Please help show me how to work this problem out..Thank you...
solve equation using the quadratic formula
1/3x^2 + 2/9x - 1 = 0
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1%2F3x%5E2+%2B+2%2F9x+-+1+=+0
Multiply by 9
3x%5E2+%2B+2x+-+9+=+0
*
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B2x%2B-9+=+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=%282%29%5E2-4%2A3%2A-9=112.

Discriminant d=112 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+112+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+112+%29%29%2F2%5C3+=+1.43050087404306
x%5B2%5D+=+%28-%282%29-sqrt%28+112+%29%29%2F2%5C3+=+-2.09716754070973

Quadratic expression 3x%5E2%2B2x%2B-9 can be factored:
3x%5E2%2B2x%2B-9+=+%28x-1.43050087404306%29%2A%28x--2.09716754070973%29
Again, the answer is: 1.43050087404306, -2.09716754070973. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B2%2Ax%2B-9+%29

The solver gets it wrong when the coeff of the x^2 is not 1, so ignore the factors.
---------------
It's (-1 + sqrt(7))/3 and
(-1 - sqrt(7))/3








Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x using the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
%281%2F3%29x%5E2%2B%282%2F9%29x-1+=+0 First, multiply through by the LCD (9) to clear the fractions.
3x%5E2%2B2x-9+=+0 Now you have: a = 3, b = 2, and c = -9. Make these substitutions into the quadratic formula:
x+=+%28-2%2B-sqrt%282%5E2-4%283%29%28-9%29%29%29%2F2%283%29 Simplify.
x+=+%28-2%2B-sqrt%284-%28-108%29%29%29%2F6
x+=+%28-2%2B-sqrt%28112%29%29%2F6
x+=+-%282%2F6%29%2Bsqrt%2816%2A7%29%29%2F6 or x+=+-%282%2F6%29-sqrt%2816%2A7%29%2F6 and these can be simplified to:
x+=+-%281%2F3%29%2B%282%2F3%29sqrt%287%29 or x+=+-%281%2F3%29-%282%2F3%29sqrt%287%29

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is:
%281%2F3%29x%5E2+%2B+%282%2F9%29x+-+1+=+0
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quadratic formula is x = %28-b+%2B-+root%282%2Cb%5E2-4ac%29%29%2F%282a%29
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standard form of the quadratic equation is ax%5E2+%2B+bx+%2B+c+=+0
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you can make your calculations easier by multiplying each side of the equation by 9.
this will remove the denominators.
since the right side of the equation was 0, it will remain 0.
doing that, your formula becomes:
3x%5E2+%2B+2x+-+9+=+0
comparing to the standard form, you get
a = 3
b = 2
c = -9
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plugging these values into the quadratic formula, you get:
x = %28-%282%29+%2B-+root%282%2C%282%29%5E2-4%2A%283%29%2A%28-9%29%29%29%2F%282%2A%283%29%29
your answer is:
x = 1.430500874
or:
x = -2.097167541
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plugging these values into your original equations proves these values are good if the equation stays true.
it does.
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it is much easier to see if you have an equation that factors easily.
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take (x-1)*(x+2) = 0
these factors are chosen so that the resulting equation factors easier when using the quadratic equation to solve it.
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the resulting equation becomes x^2 +x-2=0
use the quadratic formula to solve this:
a = 1
b = 1
c = -2
quadratic formula of x = %28-b+%2B-+root%282%2Cb%5E2-4ac%29%29%2F%282a%29
becomes: x = %28-%281%29+%2B-+root%282%2C%281%29%5E2-4%2A%281%29%2A%28-2%29%29%29%2F%282%2A%281%29%29
this becomes: x = %28-%281%29+%2B-+root%282%2C9%29%29%2F%282%2A%281%29%29
which becomes: x = %28-%281%29+%2B-+3%29%2F%282%29
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x = (-1+3)/2 = 1
or:
x = (-1-3)/2 = -2
if x = 1, then (x-1) = 0
if x = -2, then (x+2) = 0
these are the factors you started with in creating this problem so the answers come out good.