Final answer:
To solve the quadratic equation by completing the square, isolate the x terms by moving the constant term to the other side. Make the left side a perfect square by adding a term equal to half the coefficient of x squared. Factor the left side as a perfect square and take the square root of both sides to solve for x.
Step-by-step explanation:
To solve the quadratic equation by completing the square, the next step is to isolate the x terms by moving the constant term to the other side of the equation. In this case, rewrite the equation as:
x²+0.0211x = 0.0211
Now, we want to make the left side of the equation a perfect square. To do this, we take half of the coefficient of x (0.0211/2 = 0.01055), square it, and add it to both sides of the equation:
x²+0.0211x + (0.01055)² = 0.0211 + (0.01055)²
Simplifying further:
x²+0.0211x + 0.0001109 = 0.0212381
The next step is to factor the left side of the equation as a perfect square:
(x + 0.01055)² = 0.0212381
Finally, take the square root of both sides and solve for x, considering both positive and negative roots:
x + 0.01055 = ±√(0.0212381)
x = -0.01055 ± √(0.0212381)
Therefore, the two solutions are:
x = -0.01055 + √(0.0212381) and x = -0.01055 - √(0.0212381)