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Simplifying 3x2 + -82.74x + 570.4923 = 0 Reorder the terms: 570.4923 + -82.74x + 3x2 = 0 Solving 570.4923 + -82.74x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 190.1641 + -27.58x + x2 = 0 Move the constant term to the right: Add '-190.1641' to each side of the equation. 190.1641 + -27.58x + -190.1641 + x2 = 0 + -190.1641 Reorder the terms: 190.1641 + -190.1641 + -27.58x + x2 = 0 + -190.1641 Combine like terms: 190.1641 + -190.1641 = 0.0000 0.0000 + -27.58x + x2 = 0 + -190.1641 -27.58x + x2 = 0 + -190.1641 Combine like terms: 0 + -190.1641 = -190.1641 -27.58x + x2 = -190.1641 The x term is -27.58x. Take half its coefficient (-13.79). Square it (190.1641) and add it to both sides. Add '190.1641' to each side of the equation. -27.58x + 190.1641 + x2 = -190.1641 + 190.1641 Reorder the terms: 190.1641 + -27.58x + x2 = -190.1641 + 190.1641 Combine like terms: -190.1641 + 190.1641 = 0.0000 190.1641 + -27.58x + x2 = 0.0000 Factor a perfect square on the left side: (x + -13.79)(x + -13.79) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + -13.79) equal to 0.0000 and 0.0000.Subproblem 1
x + -13.79 = 0.0000 Simplifying x + -13.79 = 0.0000 Reorder the terms: -13.79 + x = 0.0000 Solving -13.79 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.79' to each side of the equation. -13.79 + 13.79 + x = 0.0000 + 13.79 Combine like terms: -13.79 + 13.79 = 0.00 0.00 + x = 0.0000 + 13.79 x = 0.0000 + 13.79 Combine like terms: 0.0000 + 13.79 = 13.79 x = 13.79 Simplifying x = 13.79Subproblem 2
x + -13.79 = 0.0000 Simplifying x + -13.79 = 0.0000 Reorder the terms: -13.79 + x = 0.0000 Solving -13.79 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.79' to each side of the equation. -13.79 + 13.79 + x = 0.0000 + 13.79 Combine like terms: -13.79 + 13.79 = 0.00 0.00 + x = 0.0000 + 13.79 x = 0.0000 + 13.79 Combine like terms: 0.0000 + 13.79 = 13.79 x = 13.79 Simplifying x = 13.79Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.79, 13.79}
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