Solve by completing the square. $\newline$ $x^2 - 28x = -11$ $\newline$ 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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Solve a quadratic equation by completing the square

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Q. Solve by completing the square.

\newline

x^2 - 28x = -11

\newline

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

\newline

x =

_____ or

x =

_____

Move Constant Term: To complete the square, we need to form a perfect square trinomial on the left side of the equation. We start by moving the constant term to the right side of the equation. $\newline$ $x^2 - 28x + \_\_\_ = -11 + \_\_\_$
Find Completing Number: To find the number to complete the square, we take half of the coefficient of $x$ , which is $-28$ , and square it. $(-28/2)^2 = (-14)^2 = 196$
Add Completing Number: Add $196$ to both sides of the equation to complete the square. $\newline$ $x^2 - 28x + 196 = -11 + 196$
Simplify Right Side: Simplify the right side of the equation. $x^2 - 28x + 196 = 185$
Factor Perfect Square Trinomial: Now we have a perfect square trinomial on the left side, which factors to $(x - 14)^2$ . $(x - 14)^2 = 185$
Take Square Root: Take the square root of both sides of the equation to solve for $x$ . $x - 14 = \pm\sqrt{185}$
Isolate $x$ : Add $14$ to both sides of the equation to isolate $x$ . $x = 14 \pm \sqrt{185}$
Approximate Square Root: Since $\sqrt{185}$ cannot be simplified to an integer or a simple fraction, we can leave it as a square root or approximate it as a decimal. $\newline$ $\sqrt{185} \approx 13.60$ (rounded to the nearest hundredth)
Write Final Solutions: Write the final solutions, using the approximation for the square root if necessary. $\newline$ $x = 14 + \sqrt{185}$ or $x = 14 - \sqrt{185}$ $\newline$ $x \approx 14 + 13.60$ or $x \approx 14 - 13.60$ $\newline$ $x \approx 27.60$ or $x \approx 0.40$