SOLUTION: x+3=square root of x+15

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Question 96890: x+3=square root of x+15
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B3=sqrt%28x%2B15%29 Start with the given equation


%28x%2B3%29%5E2=x%2B15 Square both sides


x%5E2%2B6x%2B9=x%2B15 Foil


x%5E2%2B5x-6=0 Get all terms to one side




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%2B5%2Ax-6=0 ( notice a=1, b=5, and c=-6)

x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29 Plug in a=1, b=5, and c=-6



x+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A-6+%29%29%2F%282%2A1%29 Square 5 to get 25



x+=+%28-5+%2B-+sqrt%28+25%2B24+%29%29%2F%282%2A1%29 Multiply -4%2A-6%2A1 to get 24



x+=+%28-5+%2B-+sqrt%28+49+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-5+%2B-+7%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-5+%2B-+7%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-5+%2B+7%29%2F2 or x+=+%28-5+-+7%29%2F2

Lets look at the first part:

x=%28-5+%2B+7%29%2F2

x=2%2F2 Add the terms in the numerator
x=1 Divide

So one answer is
x=1



Now lets look at the second part:

x=%28-5+-+7%29%2F2

x=-12%2F2 Subtract the terms in the numerator
x=-6 Divide

So another answer is
x=-6

So our possible solutions are:
x=1 or x=-6



Let's check them:


Let's check the solution x=-6
x%2B3=sqrt%28x%2B15%29 Start with the given equation


-6%2B3=sqrt%28-6%2B15%29 Plug in x=-6


-3=sqrt%289%29 Combine like terms


-3=3 Take the square root of 9. Since this is not true, x=-6 is not a solution (it's extraneous)


Let's check the solution x=1

x%2B3=sqrt%28x%2B15%29 Start with the given equation


1%2B3=sqrt%281%2B15%29 Plug in x=1


4=sqrt%2816%29 Combine like terms


4=4 Take the square root of 16. Since this is true, x=1 is a solution



So our only solution is x=1

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B3=sqrt%28x%2B15%29
Square both sides. %28x%2B3%29%5E2=x%2B15
x%5E2%2B6x%2B9=x%2B15
subtract x+15 from both sides. x%5E2%2B5x-6=0
(x-1)(x+6)=0
x=1 x=-6
Check:
1%2B3=sqrt%281%2B15%29 ok
-6%2B3=sqrt%28-6%2B15%29
-3%3C%3E3
x=1 is the only correct answer.
Ed