Question

Math

Posted 5 months ago

```
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) $x=\frac{-4 \pm \sqrt{34}}{3}$
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

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.

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