Solve by completing the square. $\newline$ $y^2 + 6y = 5$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $y =$ _ or $y =$ _

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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

y^2 + 6y = 5

\newline

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

\newline

y =

_____ or

y =

_____

Write equation in form: Write the equation in the form of $y^2 + by = c$ . The given equation is already in this form: $y^2 + 6y = 5$ .
Move constant term: Move the constant term to the right side of the equation. $\newline$ Subtract $5$ from both sides to isolate the $y$ terms. $\newline$ $y^2 + 6y - 5 = 0$ $\newline$ $y^2 + 6y = 5$
Complete the square: Complete the square by adding the square of half the coefficient of $y$ to both sides. $\newline$ The coefficient of $y$ is $6$ , so half of it is $3$ , and the square of $3$ is $9$ . $\newline$ Add $9$ to both sides of the equation. $\newline$ $y^2 + 6y + 9 = 5 + 9$ $\newline$ $y^2 + 6y + 9 = 14$
Factor left side: Factor the left side of the equation. $\newline$ The left side is a perfect square trinomial. $\newline$ $(y + 3)^2 = 14$
Take square root: Take the square root of both sides of the equation. $\newline$ Remember to consider both the positive and negative square roots. $\newline$ $\sqrt{(y + 3)^2} = \pm\sqrt{14}$ $\newline$ y + $3$ = $\pm\sqrt{14}$
Solve for y: Solve for y by isolating it on one side of the equation. $\newline$ Subtract $3$ from both sides to solve for y. $\newline$ $y + 3 - 3 = \pm\sqrt{14} - 3$ $\newline$ $y = -3 \pm\sqrt{14}$
Approximate square root: Approximate the square root of $14$ to the nearest hundredth and solve for $y$ . $\sqrt{14} \approx 3.74$ (rounded to the nearest hundredth) $\$y \approx -3 + 3.74$ or y \approx $-3$ - $3$ . $74$ \) $\$y \approx 0.74$ or y \approx $-6$ . $74$ \)