SOLUTION: solve the following equations for x. A) (x)(x)/(0.500-x) = 8.30 B) 2.94=(2.00 x)2/(0.200-x) C) x2/0.20+x)(0.030+x) = 2.00 D) 4.00x2/(0.100-x)(0.200-x) = 1.45

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: solve the following equations for x. A) (x)(x)/(0.500-x) = 8.30 B) 2.94=(2.00 x)2/(0.200-x) C) x2/0.20+x)(0.030+x) = 2.00 D) 4.00x2/(0.100-x)(0.200-x) = 1.45      Log On


   

Question 336529: solve the following equations for x.
A)
(x)(x)/(0.500-x) = 8.30
B)
2.94=(2.00 x)2/(0.200-x)
C)
x2/0.20+x)(0.030+x) = 2.00
D)
4.00x2/(0.100-x)(0.200-x) = 1.45
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
(x)(x)/(0.500-x) = 8.30
x^2/(.5-x)=8.3
x^2=8.3(.5-x)
x^2=4.15-8.3x
x^2+8.3x-4.15=0
x=-8.773..., x=0.4730... (see below)
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8.3x%2B-4.15+=+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=%288.3%29%5E2-4%2A1%2A-4.15=85.49.

Discriminant d=85.49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8.3%2B-sqrt%28+85.49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288.3%29%2Bsqrt%28+85.49+%29%29%2F2%5C1+=+0.473040125285524
x%5B2%5D+=+%28-%288.3%29-sqrt%28+85.49+%29%29%2F2%5C1+=+-8.77304012528553

Quadratic expression 1x%5E2%2B8.3x%2B-4.15 can be factored:
1x%5E2%2B8.3x%2B-4.15+=+1%28x-0.473040125285524%29%2A%28x--8.77304012528553%29
Again, the answer is: 0.473040125285524, -8.77304012528553. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8.3%2Ax%2B-4.15+%29