Solve by completing the square. $\newline$ $y^2 + 30y - 41 = 0$ $\newline$ 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 + 30y - 41 = 0

\newline

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

\newline

y =

_____ or

y =

_____

Rewrite Equation Form: $y^2 + 30y − 41 = 0$ $\newline$ Rewrite the equation in the form of $y^2 + by = c$ . $\newline$ Add $41$ to both sides to set the equation up for completing the square. $\newline$ $y^2 + 30y − 41 + 41 = 0 + 41$ $\newline$ $y^2 + 30y = 41$
Add $41$ Completing Square: $y^2 + 30y = 41$ $\newline$ Choose the number to add to both sides to complete the square. $\newline$ Since $(30/2)^2 = 225$ , add $225$ to both sides. $\newline$ $y^2 + 30y + 225 = 41 + 225$ $\newline$ $y^2 + 30y + 225 = 266$
Choose Number Complete Square: $y^2 + 30y + 225 = 266$ $\newline$ Identify the equation after factoring the left side. $\newline$ $y^2 + 30y + 225 = 266$ $\newline$ $(y + 15)^2 = 266$
Identify Factored Equation: y + \(15)^ $2$ = $266$ \ Identify the equation after taking the square root on both sides. Take the square root of both sides of the equation. \sqrt{(y + $15$ )^ $2$ } = \sqrt{ $266$ }\ y + $15$ = \pm\sqrt{ $266$ }
Identify After Square Root: We found: $\newline$ $y + 15 = \pm\sqrt{266}$ $\newline$ Choose the equation after isolating the variable $y$ . $\newline$ To isolate $y$ , subtract $15$ from both sides of the equation. $\newline$ $y + 15 - 15 = \pm\sqrt{266} - 15$ $\newline$ $y = -15 \pm \sqrt{266}$
Isolate Variable $y$ : We have: $y = -15 \pm \sqrt{266}$ What are the two values of $y$ ? $y = -15 + \sqrt{266}$ implies $y \approx -15 + 16.31$ . $y = -15 - \sqrt{266}$ implies $y \approx -15 - 16.31$ . Values of $y$ : $1.31$ , $-31.31$