Final answer:
Completing the square is a method to solve quadratic equations, which involves forming a perfect square trinomial to simplify the equation and make it easier to solve for the variable.
Step-by-step explanation:
The formula for completing the square is a technique used to solve quadratic equations of the form ax²+bx+c = 0. To complete the square, you need to form a perfect square trinomial on one side of the equation, which will simplify the solving process. Here's a step-by-step explanation:
Begin with the general form of a quadratic equation: ax²+bx+c = 0.
If a≠1, divide the entire equation by a to get the coefficient of x² to be 1.
Rewrite the equation with the x-terms on one side and the constant on the other: x² + (b/a)x = -c/a.
Find the number that completes the square for the x-terms. This is (b/2a)².
Add and subtract this number on the left side of the equation.
Rearrange the equation to get the perfect square trinomial on one side: (x + b/2a)².
Simplify the other side of the equation, and then solve for x by taking the square root of both sides.
Using this method, we can easily solve equations like x² + 0.0211x - 0.0211 = 0 by creating a perfect square that facilitates finding the value of x.