SOLUTION: 29=3(5r+1)2r

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Question 719495: 29=3(5r+1)2r
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
since 29 is prime, there is no rational number r to make this equation true. So we invoke the quadratic solver:

a=30, b=6, c=-29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 30x%5E2%2B6x%2B-29+=+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=%286%29%5E2-4%2A30%2A-29=3516.

Discriminant d=3516 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+3516+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+3516+%29%29%2F2%5C30+=+0.888264472024906
x%5B2%5D+=+%28-%286%29-sqrt%28+3516+%29%29%2F2%5C30+=+-1.08826447202491

Quadratic expression 30x%5E2%2B6x%2B-29 can be factored:
30x%5E2%2B6x%2B-29+=+30%28x-0.888264472024906%29%2A%28x--1.08826447202491%29
Again, the answer is: 0.888264472024906, -1.08826447202491. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+30%2Ax%5E2%2B6%2Ax%2B-29+%29