To find the solutions to the equation [tex]\(2x^2 = -10x + 12\)[/tex], we first need to rewrite it in standard quadratic form [tex]\(ax^2 + bx + c = 0\)[/tex]. Here are the steps:
1. Starting with the equation:
[tex]\[
2x^2 = -10x + 12
\][/tex]
2. Bring all terms to one side to set the equation to zero:
[tex]\[
2x^2 + 10x - 12 = 0
\][/tex]
Now we have a standard form quadratic equation:
[tex]\[
2x^2 + 10x - 12 = 0
\][/tex]
The next step is to solve this quadratic equation, either by factoring, completing the square, or using the quadratic formula. The typical quadratic formula is given by:
[tex]\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\][/tex]
where [tex]\( a = 2 \)[/tex], [tex]\( b = 10 \)[/tex], and [tex]\( c = -12 \)[/tex].
However, knowing the results directly, we see the solutions to the equation [tex]\(2x^2 + 10x - 12 = 0\)[/tex] are:
[tex]\[
x = -6 \quad \text{and} \quad x = 1
\][/tex]
Thus, the solutions to the given quadratic equation [tex]\(2x^2 + 10x - 12 = 0 \)[/tex] are:
[tex]\[
x = -6 \quad \text{and} \quad x = 1
\][/tex]
Among the options given:
[tex]\[
x = -3, x = 1, x = 3, x = 6, x = -2, x = -6
\][/tex]
the correct solutions are:
[tex]\[
x = -6 \quad \text{and} \quad x = 1
\][/tex]
