SOLUTION: Please help me solve this problem: sqrt (29-x)= x+1

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Question 877641: Please help me solve this problem: sqrt (29-x)= x+1
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Raise both sides to power of 2.
Simplify.

You found x=4 or x=-7 but the key said just x=4.
Let us see what we can find.

%28sqrt%2829-x%29%29%5E2=%28x%2B1%29%5E2
29-x=x%5E2%2B2x%2B1
0=x%5E2%2B2x%2B1-29%2Bx
x%5E2%2B3x-28=0---- Is that left member factorable?
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(x+4)(x-7), this one does not work;
(x-4)(x+7), this one works;
%28x-4%29%28x%2B7%29=0
One of the factors is zero or the other factor is zero.
x=4, OR x=-7
Both solutions will work.

CHECK:
sqrt%2829-4%29=4%2B1
sqrt%2825%29=5, Yes, x=4 works.
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sqrt%2829-%28-7%29%29=-7%2B1
sqrt%2836%29=-6
sqrt%286%2A6%29=6 or-inclusive sqrt%286%2A6%29=-6 actually; so yes, this x=-7 also will work.
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Both solutions are correct.
6%2A6=36 AND %28-6%29%28-6%29=36