SOLUTION: I have to solve using the quadratic formula 2/x + 5/x+2 = 1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I have to solve using the quadratic formula 2/x + 5/x+2 = 1      Log On


   

Question 243356: I have to solve using the quadratic formula
2/x + 5/x+2 = 1
Found 2 solutions by edjones, checkley77:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2/x + 5/(x+2) = 1 Use parentheses to help tutors.
2(x+2)+5x=x(x+2) multiply each side by x(x+2) (LCM) to eliminate fractions.
2x+4+5x=x^2+2x
7x+4=x^2+2x
x^2-5x-4=0
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B-4+=+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=%28-5%29%5E2-4%2A1%2A-4=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+41+%29%29%2F2%5C1+=+5.70156211871642
x%5B2%5D+=+%28-%28-5%29-sqrt%28+41+%29%29%2F2%5C1+=+-0.701562118716424

Quadratic expression 1x%5E2%2B-5x%2B-4 can be factored:
1x%5E2%2B-5x%2B-4+=+1%28x-5.70156211871642%29%2A%28x--0.701562118716424%29
Again, the answer is: 5.70156211871642, -0.701562118716424. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-4+%29

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
2/x+5/(x+2)=1
[2(x+2)+5x]/x(x+2)=1
[2x+4+5x]/(x^2+2x)=1
[7x+4]/(x^2+2x)=1
7x+4=x^2+2x
x^2-2x-7x-4=0
x^2-9x-4=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=(9+-sqrt[-9^2-4*1*-4])/2*1
x=(9+-sqrt[81+16])/2
x=(9+-sqrt97)/2
x=(9+-9.85)/2
x=(9+9.85)/2
x=18.85/2
x=9.424 ans
x=(9-9.85)/2
x=-.85/2
x=-.424 ans.