Solve using the quadratic formula. $\newline$ $p^2 - 7p + 5 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $p =$ _ or $p =$ _

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Solve a quadratic equation using the quadratic formula

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Q. Solve using the quadratic formula.

\newline

p^2 - 7p + 5 = 0

\newline

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

\newline

p =

_____ or

p =

_____

Quadratic Formula Coefficients: The quadratic formula is given by $p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients from the quadratic equation $ap^2 + bp + c = 0$ . In this case, $a = 1$ , $b = -7$ , and $c = 5$ .
Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . Here, it is $(-7)^2 - 4(1)(5) = 49 - 20 = 29$ .
Apply Quadratic Formula: Since the discriminant is positive, there will be two real and distinct solutions for $p$ . Now, apply the quadratic formula with the calculated discriminant.
Calculate Solutions: Calculate the two solutions using the quadratic formula: $\newline$ $p = \frac{-(-7) \pm \sqrt{29}}{2 \times 1}$ $\newline$ $p = \frac{7 \pm \sqrt{29}}{2}$
Express Solutions as Decimals: The two solutions are: $\newline$ $p = \frac{7 + \sqrt{29}}{2}$ and $p = \frac{7 - \sqrt{29}}{2}$ $\newline$ These cannot be simplified to integers or proper fractions, so we will express them as decimals rounded to the nearest hundredth.
Express Solutions as Decimals: The two solutions are: $\newline$ p = $(7 + \sqrt{29}) / 2$ and p = $(7 - \sqrt{29}) / 2$ $\newline$ These cannot be simplified to integers or proper fractions, so we will express them as decimals rounded to the nearest hundredth.Calculate the decimal values: $\newline$ p = $(7 + \sqrt{29}) / 2 \approx (7 + 5.39) / 2 \approx 12.39 / 2 \approx 6.20$ (rounded to the nearest hundredth) $\newline$ p = $(7 - \sqrt{29}) / 2 \approx (7 - 5.39) / 2 \approx 1.61 / 2 \approx 0.80$ (rounded to the nearest hundredth)