Solve by completing the square. $\newline$ $w^2 + 12w - 19 = 0$ $\newline$ 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 + 12w - 19 = 0

\newline

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

\newline

w =

_____ or

w =

_____

Rewrite Equation: $w^2 + 12w - 19 = 0$ $\newline$ Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Add $19$ to both sides to move the constant term to the right side of the equation. $\newline$ $w^2 + 12w = 19$
Complete the Square: $w^2 + 12w = 19$ $\newline$ Choose the number to add to both sides to complete the square. $\newline$ Since $(12/2)^2 = 36$ , add $36$ to both sides. $\newline$ $w^2 + 12w + 36 = 19 + 36$ $\newline$ $w^2 + 12w + 36 = 55$
Factor Left Side: $w^2 + 12w + 36 = 55$ $\newline$ Identify the equation after factoring the left side. $\newline$ $w^2 + 12w + 36 = 55$ $\newline$ $(w + 6)^2 = 55$
Take Square Root: $(w + 6)^2 = 55$ $\newline$ Identify the equation after taking the square root on both sides. $\newline$ Take the square root of both sides of the equation. $\newline$ $\sqrt{(w + 6)^2} = \pm\sqrt{55}$ $\newline$ w + $6$ = $\pm\sqrt{55}$
Isolate Variable: We found: $\newline$ $w + 6 = \pm\sqrt{55}$ $\newline$ Choose the equation after isolating the variable w. $\newline$ To isolate w, subtract $6$ from both sides of the equation. $\newline$ $w + 6 - 6 = \pm\sqrt{55} - 6$ $\newline$ $w = -6 \pm \sqrt{55}$
Find Values of w: We have: $\newline$ $w = -6 \pm \sqrt{55}$ $\newline$ What are the two values of $w$ ? $\newline$ $w = -6 + \sqrt{55}$ implies $w \approx -6 + 7.42$ which is $w \approx 1.42$ . $\newline$ $w = -6 - \sqrt{55}$ implies $w \approx -6 - 7.42$ which is $w \approx -13.42$ . $\newline$ Values of $w$ : $1.42$ , $w$ $0$