Solve by completing the square. $\newline$ $r^2 - 2r - 5 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $r =$ _ or $r =$ _

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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

r^2 - 2r - 5 = 0

\newline

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

\newline

r =

_____ or

r =

_____

Rewrite and Add: $r^2 - 2r - 5 = 0$ $\newline$ Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Add $5$ to both sides. $\newline$ $r^2 - 2r - 5 + 5 = 0 + 5$ $\newline$ $r^2 - 2r = 5$
Complete the Square: $r^2 - 2r = 5$ $\newline$ Choose the equation after completing the square. $\newline$ Since $(-2/2)^2 = 1$ , add $1$ on both sides. $\newline$ $r^2 - 2r + 1 = 5 + 1$ $\newline$ $r^2 - 2r + 1 = 6$
Factor and Identify: $r^2 - 2r + 1 = 6$ $\newline$ Identify the equation after factoring the left side. $\newline$ $r^2 - 2r + 1 = 6$ $\newline$ $(r - 1)^2 = 6$
Take Square Root: $(r - 1)^2 = 6$ $\newline$ 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. $\newline$ $\sqrt{(r - 1)^2} = \sqrt{6}$ $\newline$ $r - 1 = \pm\sqrt{6}$ $\newline$ $r - 1 \approx \pm 2.45$
Isolate Variable: We found: $\newline$ $r - 1 \approx \pm 2.45$ $\newline$ Choose the equation after isolating the variable $r$ . $\newline$ To isolate $r$ , add $1$ to both sides of the equation. $\newline$ $r - 1 + 1 \approx \pm 2.45 + 1$ $\newline$ $r \approx 1 \pm 2.45$
Isolate Variable: We found: $\newline$ $r - 1 \approx \pm 2.45$ $\newline$ Choose the equation after isolating the variable $r$ . $\newline$ To isolate $r$ , add $1$ to both sides of the equation. $\newline$ $r - 1 + 1 \approx \pm 2.45 + 1$ $\newline$ $r \approx 1 \pm 2.45$ We have: $\newline$ $r \approx 1 \pm 2.45$ $\newline$ What are the two values of $r$ ? $\newline$ $r \approx 1 + 2.45$ implies $r \approx 3.45$ . $\newline$ $r$ $0$ implies $r$ $1$ . $\newline$ Values of $r$ : $r$ $3$ , $r$ $4$