Solve using the quadratic formula. $\newline$ $g^2 - 6g - 5 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $g =$ _ or $g =$ _

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Algebra 1

Solve a quadratic equation using the quadratic formula

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Q. Solve using the quadratic formula.

\newline

g^2 - 6g - 5 = 0

\newline

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

\newline

g =

_____ or

g =

_____

Identify values: Identify the values of $a$ , $b$ , and $c$ in the quadratic equation $g^2 − 6g − 5 = 0$ . The standard form of a quadratic equation is $ax^2 + bx + c = 0$ . Comparing this with our equation, we get: $a = 1$ $b = -6$ $c = -5$
Substitute values into formula: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula to find $g$ . The quadratic formula is $g = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Here, $a = 1$ , $b = -6$ , and $c = -5$ .
Calculate discriminant: Calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . $\newline$ Discriminant = $(-6)^2 - 4(1)(-5)$ $\newline$ Discriminant = $36 + 20$ $\newline$ Discriminant = $56$
Substitute discriminant into formula: Substitute the discriminant back into the quadratic formula and simplify. $\newline$ $g = \frac{-(-6) \pm \sqrt{56}}{2 \times 1}$ $\newline$ $g = \frac{6 \pm \sqrt{56}}{2}$ $\newline$ Since $\sqrt{56}$ can be simplified to $\sqrt{4 \times 14}$ which is $2 \times \sqrt{14}$ , we get: $\newline$ $g = \frac{6 \pm 2 \times \sqrt{14}}{2}$
Simplify expression: Simplify the expression by dividing both terms in the numerator by $2$ . $g = (3 \pm \sqrt{14})$ We now have two possible solutions for $g$ .
Round values: Round the values of $g$ to the nearest hundredth, if necessary. $\newline$ $g = 3 + \sqrt{14}$ or $g = 3 - \sqrt{14}$ $\newline$ $g \approx 3 + 3.74$ or $g \approx 3 - 3.74$ $\newline$ $g \approx 6.74$ or $g \approx -0.74$