Question

Solve the following equation by factoring. Separate multiple answers with a comma.3+ 6x = 7x2AnswerKeyboax = {2

Answer 1

x={0,1,6}

Given:

`x^3+6x=7x^2`

Let us first arrange the equation and equate it to 0

`\begin{gathered} x^3+6x=7x^2 \\ x^3-7x^2+6x=0 \end{gathered}`

Factor out x:

`x(x^2-7x^{}+6)=0`

Then, factor out the quadratic equation inside the parenthesis using factoring:

`\begin{gathered} x(x^2-7x^{}+6)=0 \\ x^2-7x^{}+6=(x-6)(x-1) \\ \rightarrow x(x-6)(x-1)=0 \end{gathered}`

Now, we will equate each factor to 0 to find the solution to the equation

`\begin{gathered} x(x-6)(x-1)=0 \\ x=0 \\ ----------- \\ x-6=0 \\ x=6 \\ ----------- \\ x-1=0 \\ x=1 \end{gathered}`

Therefore, the solutions to the equation is x={0,1,6}