SOLUTION: For the function f(x)=x + 12/x , find x when f(x)=8 So I know f(x)=8 is like y=8, and I'm trying to find x. f(8)= x + 12/x Now I'm lost. Should I be multiplying both sides of

Algebra ->  Expressions-with-variables -> SOLUTION: For the function f(x)=x + 12/x , find x when f(x)=8 So I know f(x)=8 is like y=8, and I'm trying to find x. f(8)= x + 12/x Now I'm lost. Should I be multiplying both sides of      Log On


   

Question 349024: For the function f(x)=x + 12/x , find x when f(x)=8
So I know f(x)=8 is like y=8, and I'm trying to find x.
f(8)= x + 12/x
Now I'm lost. Should I be multiplying both sides of the equation by the reciprocal of 12/x?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the equation f%28x%29=%28x%2B12%29%2Fx or is it f%28x%29=x%2B12%2Fx ??? Please clarify.


Edit: Thanks for the clarification.


f%28x%29=x%2B12%2Fx Start with the given equation.


8=x%2B12%2Fx Plug in f%28x%29=8. In other words, replace f(x) with 8.


8x=x%5E2%2B12 Multiply EVERY term by x to clear out the fraction.


0=x%5E2-8x%2B12 Subtract 8x from both sides.


Notice that the quadratic x%5E2-8x%2B12 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-8, and C=12


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2812%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-8, and C=12


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2812%29+%29%29%2F%282%281%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%281%29%2812%29+%29%29%2F%282%281%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64-48+%29%29%2F%282%281%29%29 Multiply 4%281%29%2812%29 to get 48


x+=+%288+%2B-+sqrt%28+16+%29%29%2F%282%281%29%29 Subtract 48 from 64 to get 16


x+=+%288+%2B-+sqrt%28+16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%288+%2B-+4%29%2F%282%29 Take the square root of 16 to get 4.


x+=+%288+%2B+4%29%2F%282%29 or x+=+%288+-+4%29%2F%282%29 Break up the expression.


x+=+%2812%29%2F%282%29 or x+=++%284%29%2F%282%29 Combine like terms.


x+=+6 or x+=+2 Simplify.


So the solutions are x+=+6 or x+=+2


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim