Answer:
x - 2)^2 = -192
Step-by-step explanation:
Completing the square involves rewriting a quadratic equation in the standard form ax^2 + bx + c = 0 as a perfect square trinomial of the form (x - h)^2 = k. The term h is the value that completes the square in the equation x^2 + bx + c = 0, and it is found by taking half the coefficient of the x term (which is b/2).
Given the equation x^2 - 4x + 205 = 9, let's start completing the square.
1. Subtract 205 from both sides of the equation to isolate the quadratic expression on the left: x^2 - 4x = 9 - 205 = -196.
2. To complete the square, we add the square of half the coefficient of x (which is -4) to both sides. Half of -4 is -2, and (-2)^2 = 4.
The equation becomes: x^2 - 4x + 4 = -196 + 4.
This is the intermediate step in completing the square for the given equation. After simplifying the equation on the right side, it takes the form (x - 2)^2 = -192. This is the completed square for the equation. Note that the value of a in your given form (x + a)^2 = b is -2 because we have (x - 2)^2, which can also be written as (x + -2)^2.