SOLUTION: Help! Solve the equation. Square root 2x+5 minus square root x-2 = 3 What?

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Question 249025: Help!
Solve the equation.
Square root 2x+5 minus square root x-2 = 3
What?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B5%29-sqrt%28x-2%29=3 Start with the given equation.


sqrt%282x%2B5%29=3%2Bsqrt%28x-2%29 Add sqrt%28x-2%29 to both sides.


%28sqrt%282x%2B5%29%29%5E2=%283%2Bsqrt%28x-2%29%29%5E2 Square both sides.


2x%2B5=%283%2Bsqrt%28x-2%29%29%5E2 Square the square root on the left side to eliminate it.


2x%2B5=%283%2Bsqrt%28x-2%29%29%283%2Bsqrt%28x-2%29%29 Expand


2x%2B5=3%2A3%2B3%2Asqrt%28x-2%29%2B3%2Asqrt%28x-2%29%2Bsqrt%28x-2%29%2Asqrt%28x-2%29 FOIL


2x%2B5=9%2B3%2Asqrt%28x-2%29%2B3%2Asqrt%28x-2%29%2B%28sqrt%28x-2%29%29%5E2 Multiply


2x%2B5=9%2B3%2Asqrt%28x-2%29%2B3%2Asqrt%28x-2%29%2Bx-2 Square the last square root on the right side to eliminate it.



2x%2B5=7%2Bx%2B6%2Asqrt%28x-2%29 Combine like terms.


2x%2B5-7-x=6%2Asqrt%28x-2%29 Move all non square root terms to one side.


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


%28x-2%29%5E2=%286%2Asqrt%28x-2%29%29%5E2 Square both sides.


%28x-2%29%5E2=36%28x-2%29 Square 6%2Asqrt%28x-2%29 to get 36%28x-2%29


x%5E2-4x%2B4=36%28x-2%29 FOIL


x%5E2-4x%2B4=36x-72 Distribute


x%5E2-4x%2B4-36x%2B72=0 Get every term to the left side.


x%5E2-40x%2B76=0 Combine like terms.


Notice that the quadratic x%5E2-40x%2B76 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-40, and C=76


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-%28-40%29+%2B-+sqrt%28+%28-40%29%5E2-4%281%29%2876%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-40, and C=76


x+=+%2840+%2B-+sqrt%28+%28-40%29%5E2-4%281%29%2876%29+%29%29%2F%282%281%29%29 Negate -40 to get 40.


x+=+%2840+%2B-+sqrt%28+1600-4%281%29%2876%29+%29%29%2F%282%281%29%29 Square -40 to get 1600.


x+=+%2840+%2B-+sqrt%28+1600-304+%29%29%2F%282%281%29%29 Multiply 4%281%29%2876%29 to get 304


x+=+%2840+%2B-+sqrt%28+1296+%29%29%2F%282%281%29%29 Subtract 304 from 1600 to get 1296


x+=+%2840+%2B-+sqrt%28+1296+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2840+%2B-+36%29%2F%282%29 Take the square root of 1296 to get 36.


x+=+%2840+%2B+36%29%2F%282%29 or x+=+%2840+-+36%29%2F%282%29 Break up the expression.


x+=+%2876%29%2F%282%29 or x+=++%284%29%2F%282%29 Combine like terms.


x+=+38 or x+=+2 Simplify.


So the solutions are x+=+38 or x+=+2