Question

Solve the equation.√x = x-6x = [?]

Answer 1

First step, solve the square root:

`\begin{gathered} √(x)=x-6 \\ (√(x))^2=(x-6)^2 \\ x=(x-6)^2 \\ x=x^2-12x+36 \end{gathered}`

Now, we group the terms with "x" on the same side:

`\begin{gathered} x^2-12x+36-x=0 \\ x^2-13x+36=0 \end{gathered}`

Next, we use the quadratic formula to solve the equation:

`\begin{gathered} x=(13\pm√(13^2-4*36))/(2) \\ x=(13\pm√(25))/(2) \\ x=(13\pm5)/(2) \\ x=9\text{ or }x=4 \end{gathered}`

Hence, the answer is x=9 or x=4