Question

What is the solution to the equation below?A.x = 8B.x = 13C.x = 6D.x = 15

Answer 1

`x=13`

Explanation:

Solving for x,

`\begin{gathered} √(x-4)=x-10 \\ \rightarrow(√(x-4))^2=(x-10)^2 \\ \rightarrow x-4=x^2-20x+100 \\ \rightarrow x^2-21x+104=0 \\ \rightarrow(x-8)(x-13)=0 \\ \\ \rightarrow x_1=8 \\ \rightarrow x_2=13 \end{gathered}`

Now, we check the solutions to see which one is correct and which one isn't:

`\begin{gathered} √(x-4)=x-10 \\ \rightarrow√(8-4)=8-10 \\ \rightarrow√(4)=-2 \\ \rightarrow2\\e-2 \\ \\ \rightarrow√(13-4)=13-10 \\ \rightarrow√(9)=3 \\ \rightarrow3=3 \end{gathered}`

Therefore, we can conclude that the solution is:

`x=13`