Question

Solve √(x+4) = 3-√x.

Answer 1

`x=(25)/(36)`

Explanation:

Raise both sides to the power of two:

`(√(x+4)) ^(2)=(3-√(x)) ^(2)  \\x+4=(3-√(x)) ^(2)`

Expand the right side:

`x+4=9-6√(x) +x`

subtract x from both sides:

`4=9-6√(x)`

add
`6√(x)` to both sides:

`4+6√(x)=9`

Subtract 4 from both sides:

`6√(x)=5`

Divide both sides by 6:

`√(x)=(5)/(6)`

Finally. raise both sides to the power of two:

`x=((5)/(6)) ^(2) =(25)/(36)`