Question

How do you solve `\sqrt { x + 72} = x`?

Answer 1

Change the equation into a quadratic equation and use the formula to solve for x. (x=9)

Explanation:

Start off by squaring everything.

`sqrt(x+72)=x`

`x+72=x^2`

Now you can bring everything to one side of the equation.
`x^2-x-72=0`

Looking at the above equation, we can use the quadratic formula to find the value of x.
`(-b+-sqrt((b^2-4ac)))/(2a)`

Note: the values are the following:
`(ax^2+bx+c) a = 1, b=-1, c=-72`

`(1+-sqrt((-1^2-4(1)(-72))))/(2(1))`
`(1+-sqrt(289))/2`

`x=9 || x= -8`

`sqrt(9+72)=9`

`9 = 9`

`sqrt(-8+72)=-8`

`8 = -8`

-8 Doesn't work, so x must equal 9.