Final answer:
To complete the square of a quadratic equation, we adjust the equation to form a perfect square trinomial. Once in the form (x+c)²=d or (x-c)²=d, we can find the solutions for x. If given options for solutions, they must match the corresponding quadratic equation.
Step-by-step explanation:
The student has asked how to rewrite a given quadratic equation by completing the square and to find its solutions. To answer this, we need to rewrite the given quadratic equation into the form (x+c)²=d or (x-c)²=d and then solve for x.
Let's consider an example equation: x² + 0.0211x - 0.0211 = 0. To complete the square, we find a value that when added to 0.0211x makes it into a perfect square trinomial. Then we solve the resulting equation for x.
Using the quadratic formula, ax² + bx + c = 0, we can solve for x as well. Assume the solutions given as options refer to a different quadratic equation because the example doesn't match any of the options. Applying the formula, we would find the roots of the equation, which are the possible values of x that make the equation true.