Solve by completing the square. $\newline$ $p^2 + 22p - 19 = 0$ $\newline$ 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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Algebra 2

Solve a quadratic equation by completing the square

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Q. Solve by completing the square.

\newline

p^2 + 22p - 19 = 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 =

_____

Rewrite equation: $p^2 + 22p - 19 = 0$ $\newline$ Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Add $19$ to both sides. $\newline$ $p^2 + 22p - 19 + 19 = 0 + 19$ $\newline$ $p^2 + 22p = 19$
Complete the square: $p^2 + 22p = 19$ $\newline$ Choose the equation after completing the square. $\newline$ Since $(22/2)^2 = 121$ , add $121$ on both sides. $\newline$ $p^2 + 22p + 121 = 19 + 121$ $\newline$ $p^2 + 22p + 121 = 140$
Factor left side: $p^2 + 22p + 121 = 140$ $\newline$ Identify the equation after factoring the left side. $\newline$ $p^2 + 22p + 121 = 140$ $\newline$ $(p + 11)^2 = 140$
Take square root: $(p + 11)^2 = 140$ $\newline$ Identify the equation after taking the square root on both sides. $\newline$ Round the non-terminating values to the nearest hundredth. $\newline$ Take the square root of both sides of the equation. $\newline$ $\sqrt{(p + 11)^2} = \sqrt{140}$ $\newline$ $p + 11 = \pm\sqrt{140}$ $\newline$ $p + 11 \approx \pm 11.83$
Isolate variable: We found: $\newline$ $p + 11 \approx \pm 11.83$ $\newline$ Choose the equation after isolating the variable $p$ . $\newline$ To isolate $p$ , subtract $11$ from both sides of the equation. $\newline$ $p + 11 - 11 \approx \pm 11.83 - 11$ $\newline$ $p \approx -11 \pm 11.83$
Isolate variable: We found: $\newline$ $p + 11 \approx \pm 11.83$ $\newline$ Choose the equation after isolating the variable $p$ . $\newline$ To isolate $p$ , subtract $11$ from both sides of the equation. $\newline$ $p + 11 - 11 \approx \pm 11.83 - 11$ $\newline$ $p \approx -11 \pm 11.83$ We have: $\newline$ $p \approx -11 \pm 11.83$ $\newline$ What are the two values of $p$ ? $\newline$ $p \approx -11 + 11.83$ implies $p \approx 0.83$ . $\newline$ $p$ $0$ implies $p$ $1$ . $\newline$ Values of $p$ : $p$ $3$ , $p$ $4$