Solve by completing the square. $\newline$ $u^2 - 6u - 11 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $u =$ _ or $u =$ _

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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

u^2 - 6u - 11 = 0

\newline

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

\newline

u =

_____ or

u =

_____

Rewrite and Add Constant: $u^2 - 6u - 11 = 0$ $\newline$ Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Add $11$ to both sides. $\newline$ $u^2 - 6u - 11 + 11 = 0 + 11$ $\newline$ $u^2 - 6u = 11$
Complete the Square: $u^2 - 6u = 11$ $\newline$ Choose the equation after completing the square. $\newline$ Since $(-6/2)^2 = 9$ , add $9$ on both sides. $\newline$ $u^2 - 6u + 9 = 11 + 9$ $\newline$ $u^2 - 6u + 9 = 20$
Factor and Identify: $u^2 - 6u + 9 = 20$ $\newline$ Identify the equation after factoring the left side. $\newline$ $u^2 - 6u + 9 = 20$ $\newline$ $(u - 3)^2 = 20$
Take Square Root: $(u - 3)^2 = 20$ $\newline$ Identify the equation after taking the square root on both sides. $\newline$ Round the non-terminating values to the nearest hundredth. $\newline$ Take the square root of both sides of the equation. $\newline$ $\sqrt{(u - 3)^2} = \sqrt{20}$ $\newline$ $u - 3 = \pm\sqrt{20}$ $\newline$ $u - 3 \approx \pm 4.47$
Isolate Variable: We found: $\newline$ $u - 3 \approx \pm 4.47$ $\newline$ Choose the equation after isolating the variable $u$ . $\newline$ To isolate $u$ , add $3$ to both sides of the equation. $\newline$ $u - 3 + 3 \approx \pm 4.47 + 3$ $\newline$ $u \approx 3 \pm 4.47$
Isolate Variable: We found: $\newline$ $u - 3 \approx \pm 4.47$ $\newline$ Choose the equation after isolating the variable $u$ . $\newline$ To isolate $u$ , add $3$ to both sides of the equation. $\newline$ $u - 3 + 3 \approx \pm 4.47 + 3$ $\newline$ $u \approx 3 \pm 4.47$ We have: $\newline$ $u \approx 3 \pm 4.47$ $\newline$ What are the two values of $u$ ? $\newline$ $u \approx 3 + 4.47$ implies $u \approx 7.47$ . $\newline$ $u$ $0$ implies $u$ $1$ . $\newline$ Values of $u$ : $u$ $3$ , $u$ $4$