Question

What is the solution to the equation
Square root x plus 6= x

Answer 1

`√(x+6) =x`

on simplify:

x+6 = x²

x+6-x²=0

-x²+x+6=0

we change the signs

x²-x-6=0

we write -x as a difference: x²+2x-3x-6=0

we factorize:

x(x+2)-3(x+2)=0

(x+2)(x-3)=0

we solve:

x+2=0 x=-2

x-3=0 x=3

we check:

we replace x by -2:

`√(-2+6) = √(4)=2`

`√(3+6) =√(9) =3`

x-2 equality is false

solution: x=3