Question

What is the solution to the equation below. square root x + 6 = x - 6

Answer 1

`\\ \tt\rightarrowtail √(x+6)=x-6`

`\\ \tt\rightarrowtail x+6=(x-6)^2`

`\\ \tt\rightarrowtail x+6=x^2-12x+36`

`\\ \tt\rightarrowtail x^2-13x+30=0`

`\\ \tt\rightarrowtail x^2-10x-3x+30=0`

`\\ \tt\rightarrowtail (x-3)(x-10)=0`

`\\ \tt\rightarrowtail x=3,10`

Answer 2

`x = 10`

Explanation:

`√(x+6) =x-6\\`

square both sides:

`\implies x+6=(x-6)^2`

Expand brackets:

`\implies x+6=x^2-12x+36`

Collect and combine like terms:

`\implies x^2-13x+30=0`

`\implies (x-10)(x-3)=0`

`\implies x=10, x=3`

Substitute values back into original equation:

`x=10: √(10+6) =10-6 \implies 4 = 4 \ \ \checkmark`

`x=3: √(3+6) =3-6 \implies 3 = -3 \ \ \textsf{incorrect!}`

Therefore,
`x=10` only