Solve for $g$ . $\newline$ $8g^2 - 18g - 5 = 0$ $\newline$ $\newline$ Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. $\newline$ $g =$ ____ $\newline$

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Algebra 2

Solve polynomial equations

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Q. Solve for

g

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8g^2 - 18g - 5 = 0

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Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

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g =

____

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Given quadratic equation: We are given the quadratic equation $8g^2 - 18g - 5 = 0$ . To solve for $g$ , we can use the quadratic formula $g = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 8$ , $b = -18$ , and $c = -5$ .
Calculate discriminant: First, calculate the discriminant $\Delta = b^2 - 4ac$ . Here, $\Delta = (-18)^2 - 4 \times 8 \times (-5)$ .
Find square root of discriminant: Perform the calculation: $\Delta = 324 + 160 = 484$ .
Apply quadratic formula: Now, find the square root of the discriminant: $\sqrt{\Delta} = \sqrt{484} = 22$ .
Simplify expression: Apply the quadratic formula: $g = \frac{-(-18) \pm \sqrt{22}}{2 \times 8}$ .
Find two possible values for $g$ : Simplify the expression: $g = \frac{18 \pm 22}{16}$ .
Calculate first value: Find the two possible values for $g$ : $g = \frac{18 + 22}{16}$ and $g = \frac{18 - 22}{16}$ .
Simplify fraction: Calculate the first value: $g = \frac{40}{16}$ .
Calculate second value: Simplify the fraction: $g = \frac{5}{2}$ .
Simplify fraction: Calculate the second value: $g = \frac{-4}{16}$ .
Simplify fraction: Calculate the second value: $g = -\frac{4}{16}$ .Simplify the fraction: $g = -\frac{1}{4}$ .