SOLUTION: sqrtof 9x+81=x+5 not sure how to solve...please help

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Question 167316: sqrtof 9x+81=x+5
not sure how to solve...please help
Found 2 solutions by jim_thompson5910, ankor@dixie-net.com:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%289x%2B81%29=x%2B5 Start with the given equation


9x%2B81=%28x%2B5%29%5E2 Square both sides to get rid of the square root.


9x%2B81=x%5E2%2B10x%2B25 FOIL


0=x%5E2%2B10x%2B25-9x-81 Subtract 9x from both sides. Subtract 81 from both sides.


0=x%5E2%2Bx-56 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=1, and c=-56


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-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-56%29+%29%29%2F%282%281%29%29 Plug in a=1, b=1, and c=-56


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-56%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--224+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-56%29 to get -224


x+=+%28-1+%2B-+sqrt%28+1%2B224+%29%29%2F%282%281%29%29 Rewrite sqrt%281--224%29 as sqrt%281%2B224%29


x+=+%28-1+%2B-+sqrt%28+225+%29%29%2F%282%281%29%29 Add 1 to 224 to get 225


x+=+%28-1+%2B-+sqrt%28+225+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+15%29%2F%282%29 Take the square root of 225 to get 15.


x+=+%28-1+%2B+15%29%2F%282%29 or x+=+%28-1+-+15%29%2F%282%29 Break up the expression.


x+=+%2814%29%2F%282%29 or x+=++%28-16%29%2F%282%29 Combine like terms.


x+=+7 or x+=+-8 Simplify.


So the possible answers are x+=+7 or x+=+-8


However, if you plug in x+=+-8, then the equation won't be true.


=============================================

Answer:


So the only solution is x+=+7

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%289x%2B81%29 = x + 5
Square both sides:
9x + 81 = (x + 5)^2
:
FOIL the right side
9x + 81 = x^2 + 10x + 25
:
0 = x^2 + 10x - 9x + 25 - 81
:
A quadratic equation:
x^2 + x - 56 = 0
Factors to:
(x+8)(x-7) = 0
Two solutions
x = -8
and
x = 7
:
Both solutions have to be checked in the original equation:
x= -8
sqrt%289%28-8%29%2B81%29 = -8 + 5
sqrt%28-72%2B81%29 = -8 + 5
sqrt%289%29 = -3
3 does not = -3; x = -8 is not a solution
:
x=+7
sqrt%289%287%29%2B81%29 = 7 + 5
sqrt%2863%2B81%29 = 12
sqrt%28144%29 = 12
12 = 12; x=7 is good solution