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Simplifying 10x2 + -1x + -1.1 = 0 Reorder the terms: -1.1 + -1x + 10x2 = 0 Solving -1.1 + -1x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.11 + -0.1x + x2 = 0 Move the constant term to the right: Add '0.11' to each side of the equation. -0.11 + -0.1x + 0.11 + x2 = 0 + 0.11 Reorder the terms: -0.11 + 0.11 + -0.1x + x2 = 0 + 0.11 Combine like terms: -0.11 + 0.11 = 0.00 0.00 + -0.1x + x2 = 0 + 0.11 -0.1x + x2 = 0 + 0.11 Combine like terms: 0 + 0.11 = 0.11 -0.1x + x2 = 0.11 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 = 0.11 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 0.11 + 0.0025 Combine like terms: 0.11 + 0.0025 = 0.1125 0.0025 + -0.1x + x2 = 0.1125 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 0.1125 Calculate the square root of the right side: 0.335410197 Break this problem into two subproblems by setting (x + -0.05) equal to 0.335410197 and -0.335410197.Subproblem 1
x + -0.05 = 0.335410197 Simplifying x + -0.05 = 0.335410197 Reorder the terms: -0.05 + x = 0.335410197 Solving -0.05 + x = 0.335410197 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 = 0.335410197 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 0.335410197 + 0.05 x = 0.335410197 + 0.05 Combine like terms: 0.335410197 + 0.05 = 0.385410197 x = 0.385410197 Simplifying x = 0.385410197Subproblem 2
x + -0.05 = -0.335410197 Simplifying x + -0.05 = -0.335410197 Reorder the terms: -0.05 + x = -0.335410197 Solving -0.05 + x = -0.335410197 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 = -0.335410197 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -0.335410197 + 0.05 x = -0.335410197 + 0.05 Combine like terms: -0.335410197 + 0.05 = -0.285410197 x = -0.285410197 Simplifying x = -0.285410197Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.385410197, -0.285410197}
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