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Simplifying 2x2 + 0.2x + -0.01 = 0 Reorder the terms: -0.01 + 0.2x + 2x2 = 0 Solving -0.01 + 0.2x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.005 + 0.1x + x2 = 0 Move the constant term to the right: Add '0.005' to each side of the equation. -0.005 + 0.1x + 0.005 + x2 = 0 + 0.005 Reorder the terms: -0.005 + 0.005 + 0.1x + x2 = 0 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + 0.1x + x2 = 0 + 0.005 0.1x + x2 = 0 + 0.005 Combine like terms: 0 + 0.005 = 0.005 0.1x + x2 = 0.005 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.005 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.005 + 0.0025 Combine like terms: 0.005 + 0.0025 = 0.0075 0.0025 + 0.1x + x2 = 0.0075 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.0075 Calculate the square root of the right side: 0.08660254 Break this problem into two subproblems by setting (x + 0.05) equal to 0.08660254 and -0.08660254.Subproblem 1
x + 0.05 = 0.08660254 Simplifying x + 0.05 = 0.08660254 Reorder the terms: 0.05 + x = 0.08660254 Solving 0.05 + x = 0.08660254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.08660254 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.08660254 + -0.05 x = 0.08660254 + -0.05 Combine like terms: 0.08660254 + -0.05 = 0.03660254 x = 0.03660254 Simplifying x = 0.03660254Subproblem 2
x + 0.05 = -0.08660254 Simplifying x + 0.05 = -0.08660254 Reorder the terms: 0.05 + x = -0.08660254 Solving 0.05 + x = -0.08660254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.08660254 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.08660254 + -0.05 x = -0.08660254 + -0.05 Combine like terms: -0.08660254 + -0.05 = -0.13660254 x = -0.13660254 Simplifying x = -0.13660254Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.03660254, -0.13660254}
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