Question

What are the solutions to this equation? 2x^2 = -10x + 12

Answer 1

x=1 or x=-6.

Step-by-step explanation:

Given the quadratic equation:

`2x^2=-10x+12`

First, reorder the terms as follows:

`\begin{gathered} 2x^2+10x-12=0 \\ 2(x^2+5x-6)=0 \end{gathered}`

Since 2 cannot equal zero, it implies:

`x^2+5x-6=0`

Next, factorize the result obtained above.

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

The solutions to this equation are x=1 or x=-6.