Solve by completing the square. $\newline$ $w^2 + 6w = 47$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $w =$ _ or $w =$ _

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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

w^2 + 6w = 47

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

\newline

w =

_____ or

w =

_____

Write Equation Form: Write the equation in the form of $w^2 + bw = c$ . The given equation is already in this form: $w^2 + 6w = 47$ .
Move Constant Term: Move the constant term to the right side of the equation. $\newline$ Subtract $47$ from both sides to isolate the $w$ terms. $\newline$ $w^2 + 6w - 47 = 0$ $\newline$ $w^2 + 6w = 47$
Complete the Square: Complete the square by adding the square of half the coefficient of $w$ to both sides. $\newline$ Half of the coefficient of $w$ is $\frac{6}{2} = 3$ , and its square is $3^2 = 9$ . $\newline$ Add $9$ to both sides of the equation. $\newline$ $w^2 + 6w + 9 = 47 + 9$ $\newline$ $w^2 + 6w + 9 = 56$
Factor Left Side: Factor the left side of the equation. $\newline$ The left side is a perfect square trinomial. $\newline$ $(w + 3)^2 = 56$
Take Square Root: Take the square root of both sides of the equation. $\newline$ $\sqrt{(w + 3)^2} = \pm\sqrt{56}$ $\newline$ $w + 3 = \pm\sqrt{56}$
Solve for $w$ : Solve for $w$ by subtracting $3$ from both sides. $\newline$ $w = -3 \pm \sqrt{56}$ $\newline$ $w = -3 \pm \sqrt{4 \times 14}$ $\newline$ $w = -3 \pm 2\sqrt{14}$
Simplify Square Root: Simplify the square root and write the answers as decimals rounded to the nearest hundredth. $\newline$ $\sqrt{14}$ is approximately $3.74$ (rounded to the nearest hundredth). $\newline$ $w = -3 \pm 2(3.74)$ $\newline$ $w = -3 \pm 7.48$
Find Values of w: Find the two values of $w$ . $w = -3 + 7.48 \approx 4.48$ $w = -3 - 7.48 \approx -10.48$