SOLUTION: 1/x-4 +x/x-5 +1/x^2-9x+20=0 I have to solve for x I have the LCD to be(x-4)(x-5) I multiplied the numerator times the LCD and got (x-5)+x(x-4)+1=0. Next I got x-5+x^2-4x+1=0. I c

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1/x-4 +x/x-5 +1/x^2-9x+20=0 I have to solve for x I have the LCD to be(x-4)(x-5) I multiplied the numerator times the LCD and got (x-5)+x(x-4)+1=0. Next I got x-5+x^2-4x+1=0. I c      Log On


   

Question 105218: 1/x-4 +x/x-5 +1/x^2-9x+20=0 I have to solve for x I have the LCD to be(x-4)(x-5) I multiplied the numerator times the LCD and got (x-5)+x(x-4)+1=0. Next I got x-5+x^2-4x+1=0. I combined my like terms and got -3x-4+x^=0. The x ^2 keeps throwing me off because I don't know what to do with it. Please show me what to do.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to start where you left off

-3x-4%2Bx%5E2=0 Start with the given equation


x%5E2-3x-4=0 Rearrange the terms


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-3%2Ax-4=0 ( notice a=1, b=-3, and c=-4)





x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Plug in a=1, b=-3, and c=-4




x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Negate -3 to get 3




x+=+%283+%2B-+sqrt%28+9-4%2A1%2A-4+%29%29%2F%282%2A1%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)




x+=+%283+%2B-+sqrt%28+9%2B16+%29%29%2F%282%2A1%29 Multiply -4%2A-4%2A1 to get 16




x+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%283+%2B-+5%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%283+%2B-+5%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%283+%2B+5%29%2F2 or x+=+%283+-+5%29%2F2


Lets look at the first part:


x=%283+%2B+5%29%2F2


x=8%2F2 Add the terms in the numerator

x=4 Divide


So one answer is

x=4




Now lets look at the second part:


x=%283+-+5%29%2F2


x=-2%2F2 Subtract the terms in the numerator

x=-1 Divide


So another answer is

x=-1


So our solutions are:

x=4 or x=-1




However, since x=4 makes two terms of the original equation 1%2F%28x-4%29+%2Bx%2F%28x-5%29+%2B1%2F%28x%5E2-9x%2B20%29=0 have a denominator of zero, our only true solution is x=-1



So our answer is x=-1