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# How do I solve for x?

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

Guest Apr 22, 2017
#1
+1

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

30 sqrt(x) = 210

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

Raise both sides to the power of two:

Guest Apr 22, 2017
#2
+7639
+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

!

asinus  Apr 23, 2017