Final answer:
To rewrite the equation by completing the square, we add and subtract half of the coefficient of x, squared, to the equation. Then, we simplify the equation, take the square root of both sides, and solve for x. The solutions to the equation are x = -0.01055 + √(0.02087766) and x = -0.01055 - √(0.02087766).
Step-by-step explanation:
To rewrite the equation by completing the square, we first move all terms to one side to obtain:
x² + 0.0211x - 0.0211 = 0
To complete the square, we add and subtract half of the coefficient of x, squared, to the equation. In this case, the coefficient of x is 0.0211, so we add and subtract (0.0211/2)² = 0.00022166:
x² + 0.0211x + 0.00022166 - 0.0211 - 0.00022166 = 0
After simplifying, we have:
(x + 0.01055)² = 0.02087766
Now, we take the square root of both sides and solve for x:
x + 0.01055 = ±√(0.02087766)
x = -0.01055 ± √(0.02087766)
Therefore, the solutions to the equation are:
x = -0.01055 + √(0.02087766) and x = -0.01055 - √(0.02087766)