SOLUTION: Solve the equation sqrt(2x+1)+5=sqrt(x+12)-8

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Question 1033449: Solve the equation
sqrt(2x+1)+5=sqrt(x+12)-8
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Most of the work below is wrong having a mistake; I might fix and repost later:
sqrt%282x%2B1%29%2B5=sqrt%28x%2B12%29-8
sqrt%282x%2B1%29=sqrt%28x%2B12%29-8-5
sqrt%282x%2B1%29=sqrt%28x%2B12%29-13
square both sides....
2x%2B1=%28x%2B12%29-26%2Asqrt%28x%2B12%29%2B169
2x%2B1-x-12-169=-26%2Asqrt%28x%2B12%29
-2x-1%2Bx%2B12%2B169=26%2Asqrt%28x%2B12%29
-x%2B11%2B169=26sqrt%28x%2B12%29
180-x=26%2Asqrt%28x%2B12%29
Square both sides AGAIN...
676%28x%2B12%29=180%5E2-360x%2Bx%5E2
676x%2B676%2A12=x%5E2-360x%2B180%5E2
0=x%5E2-360%2B180%5E2-676x-676%2A12
x%5E2-676x-360%2B180%5E2-676%2A12=0
highlight_green%28x%5E2-676x%2B23928=0%29

You might need to check if one or both of those solutions work in the original equation.

General Solution Formula for Quadratic Equation:
x=%28676%2B-+sqrt%28676%5E2-4%2A23928%29%29%2F2
x=%28676%2B-+sqrt%28361264%29%29%2F2
-
D=16*22579=16*67*337
x=%28676%2B-+sqrt%2816%2A67%2A337%29%29%2F2
x=%28676%2B-+4%2Asqrt%2867%2A337%29%29%2F2
highlight%28cross%28x=338%2B-+2%2Asqrt%2867%2A337%29%29%29 ---------check to be sure which of these work in case only one.


*That solution is wrong. The correct results, not yet both checked, are x=24 or x=1012.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the equation
sqrt(2x+1)+5=sqrt(x+12)-8
highlight_green%28matrix%281%2C3%2C+x+=+%221%2C012%22%2C+or%2C+24%29%29, but NEITHER one satisfies the equation, so highlight_green%28matrix%281%2C3%2C+%22THERE%27S%22%2C+NO%2C+SOLUTION%29%29