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Question 98203: Can someone help me to solve the equation?
square root of x + 5 + x = 1
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Can someone help me to solve the equation?
square root of x + 5 + x = 1
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One reason that some students do not get an answer from the tutors here is that
they do not say exactly what the problem is.
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Like in this one, is it:
Sqrt(x) + 5 + x = 1
or is it:
Sqrt(x+5) + x = 1
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I am going to assume it is:
Sqrt(x+5) + x = 1
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Sqrt(x+5) = 1 - x; subtracted x from both sides
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Squaring both sides gets rid of the radical:
x + 5 = (1 - x)^2
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x + 5 = 1 - 2x + x^2; FOILed (1-x)(1-x)
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Arrange as a quadratic equation:
x^2 - 2x - x + 1 - 5 = 0
:
x^2 - 3x - 4 = 0
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This factors to:
(x - 4)(x + 1) = 0
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Two solutions:
x = +4
x = -1
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It is important to substitute both solutions in the original problem
Often only one of the solutions is valid, when a radical is involved.
Solution 1:
Sqrt(4+5) + 4 = 1
3 + 4 does not = 1, not a solution:
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Solution 2
Sqrt(-1+5) - 1 = 1
Sqrt(4) - 1 = 1;
2 - 1 = 1; a good solution
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