Question

Solve the equation.√2x = x - 4x = [? ]

Answer 1

Explanation

We are given the following equation:

`√(2x)=x-4`

We are required to determine the value of x in the given equation.

This is achieved thus:

`\begin{gathered} √(2x)=x-4 \\ \text{ Square both sides} \\ (√(2x))^2=(x-4)^2 \\ 2x=x^2-8x+16 \\ x^2-10x+16=0 \\ (x-2)(x-8)=0 \\ x-2=0;x-8=0 \\ x=2;x=8 \end{gathered}`

Substituting the values of x in the original equation, we have:

`\begin{gathered} √(2x)=x-4 \\ where\text{ }x=2 \\ √(2\cdot2)=2-4 \\ √(4)=-2 \\ 2=-2(False) \\ \\ √(2x)=x-4 \\ where\text{ }x=8 \\ √(2\cdot8)=8-4 \\ √(16)=4 \\ 4=4(True) \end{gathered}`

Hence, the answer is:

`x=8`