SOLUTION: 3+√z-10=√z+5 I need help solving radical equations please

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Question 543047: 3+√z-10=√z+5
I need help solving radical equations please
Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
Given to solve:
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Square both sides. For the left side this involves multiplying:
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and you can do this by the FOIL process to get:
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To simplify this, note that .
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Also note that
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And finally note that
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Make these changes and the squared left side becomes:
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Squaring the right side results in:
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So when both sides of this equation are squared the result is:
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Note that you have a +z on the left side and a +z on the right side. Subtracting z from both sides eliminates these two terms and you are left with:
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Combine the 9 and the -10 on the left side and you have:
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Get rid of the -1 on the left side by adding +1 to both sides to get:
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Divide both sides by 6 and the equation is then:
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Now square both sides and you have:
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Finally eliminate the -10 on the left side by adding 10 to both sides and the answer you are looking for becomes:
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You can check this out by returning to the original equation:
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and substituting 11 for z to get:
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This simplifies to:
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and taking the square roots results in:
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This is obviously true, so the answer z = 11 checks.
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Hope this helps you to understand the problem.
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