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sqrt(x+15)=15-sqrt(x)

Guest Apr 22, 2017
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 #1
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Solve for x:
sqrt(x + 15) = 15 - sqrt(x)

Raise both sides to the power of two:
x + 15 = (15 - sqrt(x))^2

Subtract (15 - sqrt(x))^2 from both sides:
15 - (15 - sqrt(x))^2 + x = 0

15 - (15 - sqrt(x))^2 + x = 30 sqrt(x) - 210:
30 sqrt(x) - 210 = 0

Add 210 to both sides:
30 sqrt(x) = 210

Divide both sides by 30:
sqrt(x) = 7

Raise both sides to the power of two:
Answer: | x = 49

Guest Apr 22, 2017
 #2
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+2

sqrt(x+15)=15-sqrt(x)

 

\(\sqrt{x+15}=15- \sqrt{x}\\x+15=225-30\sqrt{x}+x\)

 

\(30\sqrt{x}=210\\\sqrt{x}=7\)

 

x=49

 

laugh  !

asinus  Apr 23, 2017

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