Solve by completing the square. $\newline$ $v^2 + 20v - 39 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $v =$ _ or $v =$ _

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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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v^2 + 20v - 39 = 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

v =

_____ or

v =

_____

Rewrite in standard form: $v^2 + 20v - 39 = 0$ $\newline$ Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Add $39$ to both sides to set the equation up for completing the square. $\newline$ $v^2 + 20v - 39 + 39 = 0 + 39$ $\newline$ $v^2 + 20v = 39$
Add $39$ to both sides: $v^2 + 20v = 39$ $\newline$ Choose the number to add to both sides to complete the square. $\newline$ Since $(20/2)^2 = 100$ , add $100$ to both sides. $\newline$ $v^2 + 20v + 100 = 39 + 100$ $\newline$ $v^2 + 20v + 100 = 139$
Complete the square: $v^2 + 20v + 100 = 139$ $\newline$ Identify the equation after factoring the left side. $\newline$ $v^2 + 20v + 100 = 139$ $\newline$ $(v + 10)^2 = 139$
Identify factored form: $v + 10)^2 = 139(\newline$ Identify the equation after taking the square root on both sides. $\newline$ Take the square root of both sides of the equation. $\newline$ \$\sqrt{(v + 10)^2} = \sqrt{139}\)$\newline$$v + 10 = \pm\sqrt{139}$
Take square root: We found:$\newline$$v + 10 = \pm\sqrt{139}$$\newline$Choose the equation after isolating the variable $v$.$\newline$To isolate $v$, subtract $10$ from both sides of the equation.$\newline$$v + 10 - 10 = \pm\sqrt{139} - 10$$\newline$$v = -10 \pm \sqrt{139}$
Isolate variable: We have:$\newline$$v = -10 \pm \sqrt{139}$$\newline$What are the two values of $v$?$\newline$$v = -10 + \sqrt{139}$ and $v = -10 - \sqrt{139}$$\newline$Round the non-terminating values to the nearest hundredth.$\newline$$v \approx -10 + 11.79$ implies $v \approx 1.79$.$\newline$$v \approx -10 - 11.79$ implies $v \approx -21.79$.$\newline$Values of $v$: $1.79$, $v$$0$