Solve using the quadratic formula. $\newline$ $s^2 - 8s - 5 = 0$ $\newline$ 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

s^2 - 8s - 5 = 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 =

_____

Identify values: Identify the values of $a$ , $b$ , and $c$ in the quadratic equation $s^2 - 8s - 5 = 0$ . The standard form of a quadratic equation is $ax^2 + bx + c = 0$ . By comparing, we find: $a = 1$ $b = -8$ $c = -5$
Substitute into formula: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula $s = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Substitute $a = 1$ , $b = -8$ , and $c = -5$ into the quadratic formula. $s = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot 1\cdot (-5)}}{2\cdot 1}$ < $s = \frac{8 \pm \sqrt{64 + 20}}{2}$ >
Simplify expression and calculate discriminant: Simplify the expression under the square root and calculate the discriminant. $\newline$ $\sqrt{(-8)^2 - 4\cdot 1\cdot (-5)}$ $\newline$ = $\sqrt{64 + 20}$ $\newline$ = $\sqrt{84}$
Simplify quadratic formula: Simplify the quadratic formula with the calculated discriminant. $\newline$ $s = \frac{8 \pm \sqrt{84}}{2}$ $\newline$ Since $\sqrt{84}$ simplifies to $2\sqrt{21}$ , we can write: $\newline$ $s = \frac{8 \pm 2\sqrt{21}}{2}$
Calculate approximate decimal values: Simplify the expression by dividing by $2$ . $\newline$ $s = (4 \pm \sqrt{21})$ $\newline$ Now we have two possible solutions for $s$ : $\newline$ $s = 4 + \sqrt{21}$ or $s = 4 - \sqrt{21}$
Calculate approximate decimal values: Simplify the expression by dividing by $2$ . $\newline$ $s = (4 \pm \sqrt{21})$ $\newline$ Now we have two possible solutions for $s$ : $\newline$ $s = 4 + \sqrt{21}$ or $s = 4 - \sqrt{21}$ Calculate the approximate decimal values of $s$ if necessary, rounding to the nearest hundredth. $\newline$ $s \approx 4 + 4.58$ or $s \approx 4 - 4.58$ $\newline$ $s \approx 8.58$ or $s \approx -0.58$