Solve by completing the square. $\newline$ $r^2 - 18r + 49 = 0$ $\newline$ 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.

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r^2 - 18r + 49 = 0

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

\newline

r =

_____ or

r =

_____

Write equation in standard form: Write the equation in the form of $r^2 + br = c$ . The given equation is already in this form: $r^2 - 18r + 49 = 0$ .
Move constant term: Move the constant term to the other side of the equation. $\newline$ Subtract $49$ from both sides to isolate the $r$ terms. $\newline$ $r^2 - 18r = -49$
Complete the square: Complete the square by adding the square of half the coefficient of $r$ to both sides. $\newline$ The coefficient of $r$ is $-18$ , so half of it is $-9$ , and the square of $-9$ is $81$ . $\newline$ Add $81$ to both sides to complete the square. $\newline$ $r^2 − 18r + 81 = -49 + 81$ $\newline$ $r^2 − 18r + 81 = 32$
Factor left side: Factor the left side of the equation. $\newline$ The left side is a perfect square trinomial and can be factored into $(r - 9)^2$ . $\newline$ $(r - 9)^2 = 32$
Take square root: Take the square root of both sides of the equation. $\newline$ $\sqrt{(r - 9)^2} = \pm\sqrt{32}$ $\newline$ $r - 9 = \pm\sqrt{32}$
Solve for $r$ : Solve for $r$ by isolating the variable. $\newline$ Add $9$ to both sides of the equation to isolate $r$ . $\newline$ $r = 9 \pm \sqrt{32}$
Simplify and finalize: Simplify the square root and write the final answers. $\newline$ $\sqrt{32}$ can be simplified to $4\sqrt{2}$ , which is approximately $5.66$ when rounded to the nearest hundredth. $\newline$ $r = 9 \pm 4\sqrt{2}$ $\newline$ $r \approx 9 + 5.66$ or $r \approx 9 - 5.66$ $\newline$ $r \approx 14.66$ or $r \approx 3.34$