SOLUTION: how do you solve? {{{ 2sqrt(x+4)-1= x }}}

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Question 395080: how do you solve? +2sqrt%28x%2B4%29-1=+x+
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
first, isolate the radical
+2sqrt%28x%2B4%29-1=+x+
sqrt%28x%2B4%29=+%28x%2B1%29%2F2+
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next square both sides to eliminate the radical
+x%2B4=+%28x%2B1%29%5E2%2F4+
+x%2B4=+%28x%5E2%2B2x%2B1%29%2F4+
+4x%2B16=+%28x%5E2%2B2x%2B1%29 multiply both sides by 4
0=x%5E2-2x-15 gather terms on one side
0=(x-5)*(x+3) factor
x=5, or x=-3
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verify by substituting the answers into original equation
x=5:
+2sqrt%285%2B4%29-1=+5+
2*3-1=5 check
x=-3:
+2sqrt%28-3%2B4%29-1=+-3+
2-1=1 does not equal -3 so x=-3 is not a solution
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the answer is x=5