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Simplifying 100x2 + 10x + -1 = 0 Reorder the terms: -1 + 10x + 100x2 = 0 Solving -1 + 10x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.01 + 0.1x + x2 = 0 Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + 0.1x + 0.01 + x2 = 0 + 0.01 Reorder the terms: -0.01 + 0.01 + 0.1x + x2 = 0 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + 0.1x + x2 = 0 + 0.01 0.1x + x2 = 0 + 0.01 Combine like terms: 0 + 0.01 = 0.01 0.1x + x2 = 0.01 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 = 0.01 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.01 + 0.0025 Combine like terms: 0.01 + 0.0025 = 0.0125 0.0025 + 0.1x + x2 = 0.0125 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.0125 Calculate the square root of the right side: 0.111803399 Break this problem into two subproblems by setting (x + 0.05) equal to 0.111803399 and -0.111803399.Subproblem 1
x + 0.05 = 0.111803399 Simplifying x + 0.05 = 0.111803399 Reorder the terms: 0.05 + x = 0.111803399 Solving 0.05 + x = 0.111803399 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 = 0.111803399 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.111803399 + -0.05 x = 0.111803399 + -0.05 Combine like terms: 0.111803399 + -0.05 = 0.061803399 x = 0.061803399 Simplifying x = 0.061803399Subproblem 2
x + 0.05 = -0.111803399 Simplifying x + 0.05 = -0.111803399 Reorder the terms: 0.05 + x = -0.111803399 Solving 0.05 + x = -0.111803399 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 = -0.111803399 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.111803399 + -0.05 x = -0.111803399 + -0.05 Combine like terms: -0.111803399 + -0.05 = -0.161803399 x = -0.161803399 Simplifying x = -0.161803399Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.061803399, -0.161803399}
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