Question

How do you solve by completing the square `x=sqrt(x+13)+7`?

Answer 1

x=3; x=12

Rewrite it as x-7= `sqrt(x+13)`. Then square both sides and simplify,

`x^2` - 14x +49= x+13

`x^2` -15x +36=0
`x^2` -15x +`225/4` - `225/4` +36=0
(x-`15/2`)^2= `81/4`
x-`15/2` =`9/2` or `-9/2`
x= `15/2` +`9/2` or `15/2`-`9/2`
x= 12 or 3