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Simplifying 500x2 + 50x + -33 = 0 Reorder the terms: -33 + 50x + 500x2 = 0 Solving -33 + 50x + 500x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 500 the coefficient of the squared term: Divide each side by '500'. -0.066 + 0.1x + x2 = 0 Move the constant term to the right: Add '0.066' to each side of the equation. -0.066 + 0.1x + 0.066 + x2 = 0 + 0.066 Reorder the terms: -0.066 + 0.066 + 0.1x + x2 = 0 + 0.066 Combine like terms: -0.066 + 0.066 = 0.000 0.000 + 0.1x + x2 = 0 + 0.066 0.1x + x2 = 0 + 0.066 Combine like terms: 0 + 0.066 = 0.066 0.1x + x2 = 0.066 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 = 0.066 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.066 + 0.0025 Combine like terms: 0.066 + 0.0025 = 0.0685 0.0025 + 0.1x + x2 = 0.0685 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.0685 Calculate the square root of the right side: 0.261725047 Break this problem into two subproblems by setting (x + 0.05) equal to 0.261725047 and -0.261725047.Subproblem 1
x + 0.05 = 0.261725047 Simplifying x + 0.05 = 0.261725047 Reorder the terms: 0.05 + x = 0.261725047 Solving 0.05 + x = 0.261725047 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 = 0.261725047 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.261725047 + -0.05 x = 0.261725047 + -0.05 Combine like terms: 0.261725047 + -0.05 = 0.211725047 x = 0.211725047 Simplifying x = 0.211725047Subproblem 2
x + 0.05 = -0.261725047 Simplifying x + 0.05 = -0.261725047 Reorder the terms: 0.05 + x = -0.261725047 Solving 0.05 + x = -0.261725047 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 = -0.261725047 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.261725047 + -0.05 x = -0.261725047 + -0.05 Combine like terms: -0.261725047 + -0.05 = -0.311725047 x = -0.311725047 Simplifying x = -0.311725047Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.211725047, -0.311725047}
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