SOLUTION: Sqrt(5x+1)=Sqrt(x-2) +3

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Question 289122: Sqrt(5x+1)=Sqrt(x-2) +3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%285x%2B1%29=sqrt%28x-2%29%2B3 Start with the given equation.


5x%2B1=%28sqrt%28x-2%29%2B3%29%5E2 Square both sides to eliminate the square root on the left side.


5x%2B1=x-2%2B2%2A3%2Asqrt%28x-2%29%2B9 FOIL


5x%2B1=x-2%2B6%2Asqrt%28x-2%29%2B9 Multiply


5x%2B1=x%2B7%2B6%2Asqrt%28x-2%29 Combine like terms.


5x%2B1-x-7=6%2Asqrt%28x-2%29 Subtract 'x' from both sides. Subtract 7 from both sides.


4x-6=6%2Asqrt%28x-2%29 Combine like terms.


%284x-6%29%2F6=sqrt%28x-2%29 Divide both sides by 6


%28%284x-6%29%2F6%29%5E2=x-2 Square both sides to eliminate the square root on the right side.


%28%284x-6%29%5E2%29%2F%286%5E2%29=x-2 Distribute the exponent.


%28%284x-6%29%5E2%29%2F36=x-2 Square 6 to get 36.


%2816x%5E2-48x%2B36%29%2F36=x-2 FOIL


16x%5E2-48x%2B36=36%28x-2%29 Multiply both sides by 36


16x%5E2-48x%2B36=36x-72 Distribute.


16x%5E2-48x%2B36-36x%2B72=0 Get every term to the left side.


16x%5E2-84x%2B108=0 Combine like terms.


4%284x%5E2-21x%2B27%29=0 Factor out the GCF 4.


4x%5E2-21x%2B27=0 Divide both sides by 4.


Now let's use the quadratic formula to solve for 'x'.

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 4%2Ax%5E2-21%2Ax%2B27=0 ( notice a=4, b=-21, and c=27)





x+=+%28--21+%2B-+sqrt%28+%28-21%29%5E2-4%2A4%2A27+%29%29%2F%282%2A4%29 Plug in a=4, b=-21, and c=27




x+=+%2821+%2B-+sqrt%28+%28-21%29%5E2-4%2A4%2A27+%29%29%2F%282%2A4%29 Negate -21 to get 21




x+=+%2821+%2B-+sqrt%28+441-4%2A4%2A27+%29%29%2F%282%2A4%29 Square -21 to get 441 (note: remember when you square -21, you must square the negative as well. This is because %28-21%29%5E2=-21%2A-21=441.)




x+=+%2821+%2B-+sqrt%28+441%2B-432+%29%29%2F%282%2A4%29 Multiply -4%2A27%2A4 to get -432




x+=+%2821+%2B-+sqrt%28+9+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




x+=+%2821+%2B-+3%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2821+%2B-+3%29%2F8 Multiply 2 and 4 to get 8


So now the expression breaks down into two parts


x+=+%2821+%2B+3%29%2F8 or x+=+%2821+-+3%29%2F8


Lets look at the first part:


x=%2821+%2B+3%29%2F8


x=24%2F8 Add the terms in the numerator

x=3 Divide


So one answer is

x=3




Now lets look at the second part:


x=%2821+-+3%29%2F8


x=18%2F8 Subtract the terms in the numerator

x=9%2F4 Divide


So another answer is

x=9%2F4


So our solutions are:

x=3 or x=9%2F4





So the solutions to sqrt%285x%2B1%29=sqrt%28x-2%29%2B3 are x=3 or x=9%2F4. I'll let you do the check.