Solve.
$$
6+2 x^{2}-3 x=8 x^{2}
$$

Choose 1 answer:
(A) $x=3,-\frac{1}{2}$
(B) $x=\frac{5 \pm \sqrt{57}}{16}$
(C) $x=\frac{1 \pm \sqrt{17}}{-4}$
(D) $x=\frac{-4 \pm \sqrt{34}}{3}$

Question

Solve.
$$
6+2 x^{2}-3 x=8 x^{2}
$$

Choose 1 answer:
(A) $x=3,-\frac{1}{2}$
(B) $x=\frac{5 \pm \sqrt{57}}{16}$
(C) $x=\frac{1 \pm \sqrt{17}}{-4}$
(D) $x=\frac{-4 \pm \sqrt{34}}{3}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ First, we need to combine like terms and move all terms to one side of the equation to set it equal to zero: $6 + 2x^2 - 3x = 8x^2$ becomes $2x^2 - 3x + 6 - 8x^2 = 0$. ‖ ‖ step 2 ⋮ Simplify the equation by combining like terms: $2x^2 - 8x^2 = -6x^2$ and $6$ remains unchanged, so we have $-6x^2 - 3x + 6 = 0$. ‖ ‖ step 3 ⋮ Divide the entire equation by $-3$ to simplify: $\frac{-6x^2}{-3} - \frac{3x}{-3} + \frac{6}{-3} = 0$ which simplifies to $2x^2 + x - 2 = 0$. ‖ ‖ step 4 ⋮ Factor the quadratic equation: $(2x - 1)(x + 2) = 0$. ‖ ‖ step 5 ⋮ Solve for $x$ by setting each factor equal to zero: $2x - 1 = 0$ and $x + 2 = 0$. ‖ ‖ step 6 ⋮ Solve the first equation $2x - 1 = 0$ for $x$: $x = \frac{1}{2}$. ‖ ‖ step 7 ⋮ Solve the second equation $x + 2 = 0$ for $x$: $x = -2$. ‖ ***A*** ∻Key Concept∻ ⚹Solving quadratic equations by factoring⚹ ∻Explanation∻ ⚹To solve a quadratic equation, we can move all terms to one side to set the equation to zero, factor the quadratic, and then solve for $x$ by setting each factor equal to zero.⚹◊What method can be used to solve the quadratic equation $6+2x^{2}-3x=8x^{2}$?⍭ Generate me a similar question◊

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