SOLUTION: The Question: -10,000+8,000/(1+x)+5,625/(1+x)^2=0 Thank you

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Question 263761: The Question: -10,000+8,000/(1+x)+5,625/(1+x)^2=0
Thank you
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
The Question: -10,000+8,000/(1+x)+5,625/(1+x)^2=0
dont go bonkers when u look at all the numbers its the same basic of equations
im going to move them into the normal seen order {Ax^2+Bx+C=0}
-10000 + 8000/(1+x)+ 5625/((1+x)^2)= 0
First multiply everything by ((1+x)(1+x))
-10000((1+x)(1+x)) + 8000(1+x) + 5625 = 0
-10000(x^2+2x+1) + 8000x + 8000 + 5625 = 0
-10000x^2 + -20000x -10000 + 8000x + 13625 = 0
-10000x^2 + -12000x + 3625 = 0 Multiply by a -1
10000x^2 + 12000x - 3625 = 0 Divide by common factor 125
80x^2 + 96x - 29 = 0 now you have a more simplified equation to solve
A=80 B=96 C=-29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 80x%5E2%2B96x%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=%2896%29%5E2-4%2A80%2A-29=18496.

Discriminant d=18496 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-96%2B-sqrt%28+18496+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2896%29%2Bsqrt%28+18496+%29%29%2F2%5C80+=+0.25
x%5B2%5D+=+%28-%2896%29-sqrt%28+18496+%29%29%2F2%5C80+=+-1.45

Quadratic expression 80x%5E2%2B96x%2B-29 can be factored:
80x%5E2%2B96x%2B-29+=+80%28x-0.25%29%2A%28x--1.45%29
Again, the answer is: 0.25, -1.45. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+80%2Ax%5E2%2B96%2Ax%2B-29+%29