Questions: Consider the equation: x^2-2x-99=0 A) First, use the "completing the square" process to write this equation in the form (x+D)^2=E and enter your results below. x^2-2x-99=0 is equivalent to: =

Consider the equation: x^2-2x-99=0
A) First, use the "completing the square" process to write this equation in the form (x+D)^2=E and enter your results below.
x^2-2x-99=0 is equivalent to:
=

Transcript text: Consider the equation: $x^{2}-2 x-99=0$ A) First, use the "completing the square" process to write this equation in the form $(x+D)^{2}=E$ and enter your results below. $x^{2}-2 x-99=0$ is equivalent to: $\square$ \[ = \] $\square$

Solution

Solution Steps

To solve the given quadratic equation $x^2 - 2x - 99 = 0$ by completing the square, follow these steps:

Move the constant term to the right side of the equation.
Add and subtract the square of half the coefficient of $x$ to the left side.
Factor the left side as a perfect square trinomial.
Simplify the right side.

Step 1: Move the Constant Term to the Right Side

Given the equation: \[ x^2 - 2x - 99 = 0 \]

Move the constant term $-99$ to the right side: \[ x^2 - 2x = 99 \]

Step 2: Add and Subtract the Square of Half the Coefficient of $x$

The coefficient of $x$ is $-2$. Half of this coefficient is $-1$, and its square is: \[ \left( \frac{-2}{2} \right)^2 = 1 \]

Add and subtract this value on the left side: \[ x^2 - 2x + 1 - 1 = 99 \] \[ x^2 - 2x + 1 = 99 + 1 \]

Step 3: Factor the Left Side as a Perfect Square Trinomial

The left side can be factored as: \[ (x - 1)^2 = 100 \]

Final Answer

\[ \boxed{(x - 1)^2 = 100} \]

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