Solve using the quadratic formula. $\newline$ $3k^2 - 8k - 4 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $k =$ _ or $k =$ _

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Algebra 2

Solve a quadratic equation using the quadratic formula

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Q. Solve using the quadratic formula.

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3k^2 - 8k - 4 = 0

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Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

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k =

_____ or

k =

_____

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic equation $3k^2 − 8k − 4 = 0$ . Comparing $3k^2 − 8k − 4 = 0$ with the standard form $ax^2 + bx + c = 0$ , we find: $a = 3$ $b = -8$ $c = -4$
Substitute values into formula: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula, $k = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . $\newline$ The quadratic formula is $k = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot3\cdot(-4)}}{2\cdot3}$ .
Simplify expression: Simplify the expression inside the square root and the constants outside the square root. $\newline$ $k = \frac{8 \pm \sqrt{64 + 48}}{6}$ $\newline$ $k = \frac{8 \pm \sqrt{112}}{6}$
Simplify square root: Simplify the square root $\sqrt{112}$ to its simplest radical form. $\newline$ $\sqrt{112}$ can be simplified to $\sqrt{16\times7}$ , which is $4\sqrt{7}$ . $\newline$ $k = \frac{8 \pm 4\sqrt{7}}{6}$
Divide terms by denominator: Simplify the expression by dividing the terms in the numerator by the denominator. $\newline$ $k = \frac{8}{6} \pm \frac{4\sqrt{7}}{6}$ $\newline$ $k = \frac{4}{3} \pm \frac{2\sqrt{7}}{3}$
Round if necessary: If necessary, round the decimal values to the nearest hundredth. However, since the question asks for integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth, we can leave the answer in the form of fractions. $k = \frac{4}{3} + \frac{2\sqrt{7}}{3}$ or $k = \frac{4}{3} - \frac{2\sqrt{7}}{3}$