Solve using the quadratic formula. $\newline$ $4s^2 - 9s - 8 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $s =$ _ or $s =$ _

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Algebra 2

Solve a quadratic equation using the quadratic formula

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Q. Solve using the quadratic formula.

\newline

4s^2 - 9s - 8 = 0

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

\newline

s =

_____ or

s =

_____

Identify values of $a$ , $b$ , $c$ : Identify the values of $a$ , $b$ , and $c$ in the quadratic equation $4s^2 − 9s − 8 = 0$ . Compare $4s^2 − 9s − 8 = 0$ with the standard form $ax^2 + bx + c = 0$ . $a = 4$ $b$ $0$ $b$ $1$
Substitute values into formula: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula $s = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . $\newline$ Substitute $a = 4$ , $b = -9$ , and $c = -8$ into the quadratic formula. $\newline$ $s = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot4\cdot(-8)}}{2\cdot4}$ $\newline$ $s = \frac{9 \pm \sqrt{81 + 128}}{8}$
Simplify expression and calculate discriminant: Simplify the expression under the square root and calculate the discriminant. $\newline$ $\sqrt{(-9)^2 - 4\cdot4\cdot(-8)}$ $\newline$ = $\sqrt{81 + 128}$ $\newline$ = $\sqrt{209}$
Calculate two possible solutions: Calculate the two possible solutions for $s$ . $s = \frac{9 \pm \sqrt{209}}{8}$ We have two solutions: $s = \frac{9 + \sqrt{209}}{8}$ and $s = \frac{9 - \sqrt{209}}{8}$
Simplify solutions and round: Simplify the solutions and, if necessary, round to the nearest hundredth. $\newline$ First solution: $\newline$ $s = \frac{9 + \sqrt{209}}{8}$ $\newline$ Second solution: $\newline$ $s = \frac{9 - \sqrt{209}}{8}$ $\newline$ If we need to round to the nearest hundredth, we can use a calculator to find the approximate decimal values.
Approximate decimal values: Use a calculator to approximate the decimal values of $s$ . First solution: $s \approx (9 + 14.456) / 8$ $s \approx 23.456 / 8$ $s \approx 2.932$ Second solution: $s \approx (9 - 14.456) / 8$ $s \approx -5.456 / 8$ $s \approx -0.682$