Solve by completing the square. $\newline$ $x^2 + 16x = -35$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $x =$ _ or $x =$ _

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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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x^2 + 16x = -35

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

\newline

x =

_____ or

x =

_____

Rewrite equation: Rewrite the equation in the form of $x^2 + bx = c$ . We have the equation $x^2 + 16x = -35$ . To complete the square, we need to move the constant term to the other side of the equation. $x^2 + 16x + 35 = 0$
Complete the square: Choose the equation after completing the square. $\newline$ To complete the square, we need to add $(b/2)^2$ to both sides of the equation, where $b$ is the coefficient of $x$ . In this case, $b = 16$ , so $(b/2)^2 = (16/2)^2 = 8^2 = 64$ . $\newline$ $x^2 + 16x + 64 = 35 + 64$
Factor left side: Identify the equation after factoring the left side. $\newline$ Now we have a perfect square trinomial on the left side, which factors into $(x + 8)^2$ . $\newline$ $(x + 8)^2 = 99$
Take square root: Identify the equation after taking the square root on both sides. $\newline$ Take the square root of both sides of the equation to solve for $x$ . $\newline$ $\sqrt{(x + 8)^2} = \pm\sqrt{99}$ $\newline$ $x + 8 = \pm\sqrt{99}$
Isolate variable: Choose the equation after isolating the variable $x$ . $\newline$ To isolate $x$ , subtract $8$ from both sides of the equation. $\newline$ $x + 8 - 8 = \pm\sqrt{99} - 8$ $\newline$ $x = \pm\sqrt{99} - 8$
Calculate values: What are the two values of $x$ ? $\newline$ Now we need to calculate the square root of $99$ and subtract $8$ from it. The square root of $99$ is approximately $9.95$ (rounded to the nearest hundredth). $\newline$ $x \approx 9.95 - 8$ or $x \approx -9.95 - 8$ $\newline$ $x \approx 1.95$ or $x \approx -17.95$