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Simplifying 5.4x2 + -125x + -250 = 0 Reorder the terms: -250 + -125x + 5.4x2 = 0 Solving -250 + -125x + 5.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.4 the coefficient of the squared term: Divide each side by '5.4'. -46.2962963 + -23.14814815x + x2 = 0 Move the constant term to the right: Add '46.2962963' to each side of the equation. -46.2962963 + -23.14814815x + 46.2962963 + x2 = 0 + 46.2962963 Reorder the terms: -46.2962963 + 46.2962963 + -23.14814815x + x2 = 0 + 46.2962963 Combine like terms: -46.2962963 + 46.2962963 = 0.0000000 0.0000000 + -23.14814815x + x2 = 0 + 46.2962963 -23.14814815x + x2 = 0 + 46.2962963 Combine like terms: 0 + 46.2962963 = 46.2962963 -23.14814815x + x2 = 46.2962963 The x term is -23.14814815x. Take half its coefficient (-11.57407408). Square it (133.9591908) and add it to both sides. Add '133.9591908' to each side of the equation. -23.14814815x + 133.9591908 + x2 = 46.2962963 + 133.9591908 Reorder the terms: 133.9591908 + -23.14814815x + x2 = 46.2962963 + 133.9591908 Combine like terms: 46.2962963 + 133.9591908 = 180.2554871 133.9591908 + -23.14814815x + x2 = 180.2554871 Factor a perfect square on the left side: (x + -11.57407408)(x + -11.57407408) = 180.2554871 Calculate the square root of the right side: 13.425925931 Break this problem into two subproblems by setting (x + -11.57407408) equal to 13.425925931 and -13.425925931.Subproblem 1
x + -11.57407408 = 13.425925931 Simplifying x + -11.57407408 = 13.425925931 Reorder the terms: -11.57407408 + x = 13.425925931 Solving -11.57407408 + x = 13.425925931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.57407408' to each side of the equation. -11.57407408 + 11.57407408 + x = 13.425925931 + 11.57407408 Combine like terms: -11.57407408 + 11.57407408 = 0.00000000 0.00000000 + x = 13.425925931 + 11.57407408 x = 13.425925931 + 11.57407408 Combine like terms: 13.425925931 + 11.57407408 = 25.000000011 x = 25.000000011 Simplifying x = 25.000000011Subproblem 2
x + -11.57407408 = -13.425925931 Simplifying x + -11.57407408 = -13.425925931 Reorder the terms: -11.57407408 + x = -13.425925931 Solving -11.57407408 + x = -13.425925931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.57407408' to each side of the equation. -11.57407408 + 11.57407408 + x = -13.425925931 + 11.57407408 Combine like terms: -11.57407408 + 11.57407408 = 0.00000000 0.00000000 + x = -13.425925931 + 11.57407408 x = -13.425925931 + 11.57407408 Combine like terms: -13.425925931 + 11.57407408 = -1.851851851 x = -1.851851851 Simplifying x = -1.851851851Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.000000011, -1.851851851}
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