Final answer:
While completing the square for the equation x² + 0.0211x - 0.0211 = 0, none of the options provided (a-d) exactly match the resulting form after the process which should be (x + 0.01055)² = 0.02121121.
Step-by-step explanation:
The intermediate step in completing the square of the equation x² + 0.0211x - 0.0211 = 0 is to express it in the form (x + a)² = b. We first bring the constant term to the opposite side:
x² + 0.0211x = 0.0211
Next, we find the value to complete the square by taking half of the coefficient of x and squaring it:
(0.0211/2)² = 0.00011121
We add this value to both sides of the equation:
x² + 0.0211x + 0.00011121 = 0.0211 + 0.00011121
Now, the left side of the equation is a perfect square trinomial and we can express it as:
(x + 0.01055)² = 0.02121121
For the provided options, after completing the square process, the equation should look like one of these forms depending on the value of 'a' and 'b' in the equation. But none of the options provided align perfectly with the result of completing the square for the given equation.