SOLUTION: Change to quadratic equation then find the solution set. Please help me solve this. {{{ 6 over s+5 + s-5 over 2x=x-1 }}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Change to quadratic equation then find the solution set. Please help me solve this. {{{ 6 over s+5 + s-5 over 2x=x-1 }}}      Log On


   

Question 981397: Change to quadratic equation then find the solution set.
Please help me solve this.
+6+over+s%2B5+%2B+s-5+over+2x=x-1+
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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Your equation is difficult to understand.
If the equation below is not correct, please clarify your question and re-post.
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%286%2F%28s%2B5%29%29%2B%28%28s-5%29%2F2x%29=x-1 Multiply by (s+5)(2x)
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%28%286%29%282x%29%29%2B%28s-5%29%28s%2B5%29=x-1
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12x%2Bs%5E2-25=x-1 Subtract (x-1) from each side.
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s%5E2%2B11x-24=0
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation as%5E2%2Bbs%2Bc=0 (in our case 1s%5E2%2B11s%2B-24+=+0) has the following solutons:

s%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=%2811%29%5E2-4%2A1%2A-24=217.

Discriminant d=217 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-11%2B-sqrt%28+217+%29%29%2F2%5Ca.

s%5B1%5D+=+%28-%2811%29%2Bsqrt%28+217+%29%29%2F2%5C1+=+1.86545993132812
s%5B2%5D+=+%28-%2811%29-sqrt%28+217+%29%29%2F2%5C1+=+-12.8654599313281

Quadratic expression 1s%5E2%2B11s%2B-24 can be factored:
1s%5E2%2B11s%2B-24+=+1%28s-1.86545993132812%29%2A%28s--12.8654599313281%29
Again, the answer is: 1.86545993132812, -12.8654599313281. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B11%2Ax%2B-24+%29

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ANSWERS: s=1.865 OR s=-12.865