How do you solve sqrt(x-15)=3-sqrtx and check the solution?

1 Answer
Douglas K.
Mar 16, 2017

Please see the link to WorlframAlpha; it will tell you that [No solutions exist.](http://www.wolframalpha.com/input/?i=sqrt%28x-15%29=3-sqrtx)

Explanation:

Before beginning, add the restriction that x must be greater than or equal to 15:

sqrt(x-15)=3-sqrtx;x >=15

Add sqrtx to both sides:

sqrt(x-15)+sqrtx=3;x >=15

Square both sides:

x- 15 + 2sqrt(x-15)sqrtx + x=9;x >=15

Add 15 - 2x to both sides:

2sqrt(x-15)sqrtx=26 - 2x;x >=15

Divide both sides by 2:

sqrt(x-15)sqrtx=13 - x;x >=15

Square both sides:

(x-15)x=169 - 26x + x^2;x >=15

x^2-15x=169 - 26x + x^2;x >=15

-15x=169 - 26x;x >=15

11x = 169;x>=15

x = 15.36;x>=15

But if you substitute this solution into the original equation you do not obtain equality; [No solutions exist.](http://www.wolframalpha.com/input/?i=sqrt%28x-15%29=3-sqrtx)

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