Question

How do you solve `sqrt(x^2+8x-9)=x`?

Answer 1

`x=9/8`

Explanation:

`sqrt(x^2+8x-9) = x`

Squaring both sides,
`x^2+8x-9 = x^2`

Subtracting `x^2` from both sides,
`8x-9=0`
`8x=9`
`x=9/8`

Answer 2

`x=9/8`

Explanation:

`color(blue)"square both sides"`

`rArr(sqrt(x^2+8x-9))^2=x^2`

`rArrcancel(x^2)+8x-9=cancel(x^2)`

`rArr8x=9rArrx=9/8`

`color(blue)"As a check"`

`rArrsqrt((9/8)^2+8(9/8)-9)`

`=sqrt(81/64cancel(+9)cancel(-9))=9/8=" right side"`

`rArrx=9/8" is the solution"`

Answer 3

`x=9/8`

Explanation:

We can square both sides of the equation.

`sqrt(x^2+8x-9)=x`

`x^2+8x-9=x^2`

`8x-9=0`

`8x=9`

`x=9/8`