Solve by completing the square. $\newline$ $w^2 + 26w + 37 = 0$ $\newline$ 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.

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w^2 + 26w + 37 = 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

w =

_____ or

w =

_____

Rewrite and Subtract: $w^2 + 26w + 37 = 0$ $\newline$ Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Subtract $37$ from both sides. $\newline$ $w^2 + 26w + 37 - 37 = 0 - 37$ $\newline$ $w^2 + 26w = -37$
Complete the Square: $w^2 + 26w = -37$ $\newline$ Choose the equation after completing the square. $\newline$ Since $(26/2)^2 = 169$ , add $169$ to both sides. $\newline$ $w^2 + 26w + 169 = -37 + 169$ $\newline$ $w^2 + 26w + 169 = 132$
Factor and Identify: $w^2 + 26w + 169 = 132$ $\newline$ Identify the equation after factoring the left side. $\newline$ $w^2 + 26w + 169 = 132$ $\newline$ $(w + 13)^2 = 132$
Take Square Root: $w + 13)^2 = 132(\newline$ 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 + 13)^2} = \sqrt{132}\)$\newline$$w + 13 = \pm\sqrt{132}$
Isolate Variable: We found:$\newline$$w + 13 = \pm\sqrt{132}$$\newline$Choose the equation after isolating the variable $w$.$\newline$To isolate $w$, subtract $13$ from both sides of the equation.$\newline$$w + 13 - 13 = \pm\sqrt{132} - 13$$\newline$$w = \pm\sqrt{132} - 13$
Isolate Variable: We found:$\newline$$w + 13 = \pm\sqrt{132}$$\newline$Choose the equation after isolating the variable w.$\newline$To isolate $w$, subtract $13$ from both sides of the equation.$\newline$$w + 13 - 13 = \pm\sqrt{132} - 13$$\newline$$w = \pm\sqrt{132} - 13$We have:$\newline$$w = \pm\sqrt{132} - 13$$\newline$What are the two values of $w$?$\newline$$w = \sqrt{132} - 13$ implies $w \approx 11.49 - 13$.$\newline$$w = -\sqrt{132} - 13$ implies $w$$0$.$\newline$Values of $w$: $w$$2$, $w$$3$