To solve the equation \(x^2 - 2x - 4 = 0\) by completing the square, we need to follow a series of steps. Here is the correct order of the steps along with the corresponding equations:
Step 1: Move the constant term to the right side of the equation.
[tex]\[ x^2 - 2x = 4 \][/tex]
Step 2: Add \((b/2)^2\) to both sides of the equation, where \(b\) is the coefficient of \(x\).
[tex]\[ x^2 - 2x + 1 = 4 + 1 \][/tex]
(Note: \( \frac{-2}{2} = -1 \) and \((-1)^2 = 1\).)
Step 3: Factor the left side of the equation as a square.
[tex]\[ (x - 1)^2 = 5 \][/tex]
Step 4: Take the square root of both sides of the equation.
[tex]\[ x - 1 = \pm \sqrt{5} \][/tex]
Here are the steps matched with the correct equations:
- Step 1: \( x^2 - 2x = 4 \)
- Step 2: \( x^2 - 2x + 1 = 4 + 1 \)
- Step 3: \( (x - 1)^2 = 5 \)
- Step 4: \( x - 1 = \pm \sqrt{5} \)
By following these steps, we successfully complete the square and solve the equation.
