SOLUTION: 3xsquared-25x=-28 and also x2-24x+129=0 Thank you for the help! My parents can't remember algebra.

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Question 32640: 3xsquared-25x=-28
and also
x2-24x+129=0
Thank you for the help! My parents can't remember algebra.
Answer by stanbon(48545) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2-25x+28=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-25x%2B28+=+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=%28-25%29%5E2-4%2A3%2A28=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--25%2B-sqrt%28+289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-25%29%2Bsqrt%28+289+%29%29%2F2%5C3+=+7
x%5B2%5D+=+%28-%28-25%29-sqrt%28+289+%29%29%2F2%5C3+=+1.33333333333333

Quadratic expression 3x%5E2%2B-25x%2B28 can be factored:
3x%5E2%2B-25x%2B28+=+3%28x-7%29%2A%28x-1.33333333333333%29
Again, the answer is: 7, 1.33333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-25%2Ax%2B28+%29

x^2-24x+129=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-24x%2B129+=+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=%28-24%29%5E2-4%2A1%2A129=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--24%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-24%29%2Bsqrt%28+60+%29%29%2F2%5C1+=+15.8729833462074
x%5B2%5D+=+%28-%28-24%29-sqrt%28+60+%29%29%2F2%5C1+=+8.12701665379258

Quadratic expression 1x%5E2%2B-24x%2B129 can be factored:
1x%5E2%2B-24x%2B129+=+1%28x-15.8729833462074%29%2A%28x-8.12701665379258%29
Again, the answer is: 15.8729833462074, 8.12701665379258. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-24%2Ax%2B129+%29

Hope this helps.
Cheers,
Stan H.