Solve using the quadratic formula. $\newline$ $9p^2 + 4p - 1 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $p =$ _ or $p =$ _

Full solution

Q. Solve using the quadratic formula.

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9p^2 + 4p - 1 = 0

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

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p =

_____ or

p =

_____

Identify coefficients: Identify the coefficients $a$ , $b$ , and $c$ in the quadratic equation $9p^2 + 4p - 1 = 0$ . $a = 9$ , $b = 4$ , $c = -1$
Write quadratic formula: Write down the quadratic formula: $p = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Substitute values: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula. $p = \frac{{-(4) \pm \sqrt{{(4)^2 - 4\cdot(9)\cdot(-1)}}}}{{2\cdot(9)}}$
Simplify square root: Simplify the expression under the square root ( $\sqrt{b^2 - 4ac}$ ). $\newline$ $\sqrt{(4)^2 - 4\cdot(9)\cdot(-1)} = \sqrt{16 + 36} = \sqrt{52}$
Simplify formula: Simplify the quadratic formula with the values. $p = \frac{{-4 \pm \sqrt{52}}}{{18}}$
Calculate solutions: Calculate the two possible solutions for $p$ . $p = \frac{{-4 + \sqrt{52}}}{{18}}$ or $p = \frac{{-4 - \sqrt{52}}}{{18}}$
Round values: Round the values of $p$ to the nearest hundredth, if necessary. $p \approx (-4 + 7.21) / 18$ or $p \approx (-4 - 7.21) / 18$ $p \approx 3.21 / 18$ or $p \approx -11.21 / 18$ $p \approx 0.18$ or $p \approx -0.62$