SOLUTION: Question: {{{x-2-8*sqrt(x-2) +15=0 }}} Work: {{{13=8*sqrt(x-2) -x }}} i dont know what to do next to solve for x?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Question: {{{x-2-8*sqrt(x-2) +15=0 }}} Work: {{{13=8*sqrt(x-2) -x }}} i dont know what to do next to solve for x?      Log On


   

Question 453256: Question:
x-2-8%2Asqrt%28x-2%29+%2B15=0+
Work:
13=8%2Asqrt%28x-2%29+-x+
i dont know what to do next to solve for x?
Found 2 solutions by MathLover1, pedjajov:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x-2-8%2Asqrt%28x-2%29+%2B15=0+
Work:
13%2Bx=8%2Asqrt%28x-2%29+...both sides raise to the power of two
%2813%2Bx%29%5E2=%288%2Asqrt%28x-2%29%29%5E2+
169%2B26x%2Bx%5E2=64%28x-2%29+
169%2B26x%2Bx%5E2=64x-128+

x%5E2%2B26x-64x%2B169%2B128=0+

x%5E2-38x%2B297=0+...now use quadratic formula

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%5E2-38%2Ax%2B297=0 ( notice a=1, b=-38, and c=297)





x+=+%28--38+%2B-+sqrt%28+%28-38%29%5E2-4%2A1%2A297+%29%29%2F%282%2A1%29 Plug in a=1, b=-38, and c=297




x+=+%2838+%2B-+sqrt%28+%28-38%29%5E2-4%2A1%2A297+%29%29%2F%282%2A1%29 Negate -38 to get 38




x+=+%2838+%2B-+sqrt%28+1444-4%2A1%2A297+%29%29%2F%282%2A1%29 Square -38 to get 1444 (note: remember when you square -38, you must square the negative as well. This is because %28-38%29%5E2=-38%2A-38=1444.)




x+=+%2838+%2B-+sqrt%28+1444%2B-1188+%29%29%2F%282%2A1%29 Multiply -4%2A297%2A1 to get -1188




x+=+%2838+%2B-+sqrt%28+256+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%2838+%2B-+16%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2838+%2B-+16%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%2838+%2B+16%29%2F2 or x+=+%2838+-+16%29%2F2


Lets look at the first part:


x=%2838+%2B+16%29%2F2


x=54%2F2 Add the terms in the numerator

x=27 Divide


So one answer is

x=27




Now lets look at the second part:


x=%2838+-+16%29%2F2


x=22%2F2 Subtract the terms in the numerator

x=11 Divide


So another answer is

x=11


So our solutions are:

x=27 or x=11





+graph%28+500%2C+500%2C+-50%2C+50%2C+-70%2C+300%2Cx%5E2-38x%2B297%29+





Answer by pedjajov(51) About Me  (Show Source):
You can put this solution on YOUR website!
x-2-8sqrt%28x-1%29%2B15=0, move radical on right, everything else on left
13%2Bx=8sqrt%28x-2%29, square both sides
%2813%2Bx%29%5E2=64%28x-2%29, calculate
169%2B26x%2Bx%5E2=64x-128, move everything to the left side
x%5E2%2B26x-64x%2B169%2B128=0, combine like terms
x%5E2-38x%2B297=0, we now have quadratic equation
:
x+=+%28-%28-38%29+%2B-+sqrt%28+%28-38%29%5E2-4%2A1%2A297+%29%29%2F%282%2A1%29+
x+=+%2838+%2B-+sqrt%281444-1188%29%29%2F2
x+=+%2838+%2B-+16%29%2F2+
:
x+=+%2838%2B16%29%2F2+, x = 27 or x+=+%2838-16%29%2F2+, x = 11