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Simplifying 335 = 24.6x + 0.45x2 Solving 335 = 24.6x + 0.45x2 Solving for variable 'x'. Reorder the terms: 335 + -24.6x + -0.45x2 = 24.6x + -24.6x + 0.45x2 + -0.45x2 Combine like terms: 24.6x + -24.6x = 0.0 335 + -24.6x + -0.45x2 = 0.0 + 0.45x2 + -0.45x2 335 + -24.6x + -0.45x2 = 0.45x2 + -0.45x2 Combine like terms: 0.45x2 + -0.45x2 = 0.00 335 + -24.6x + -0.45x2 = 0.00 Begin completing the square. Divide all terms by -0.45 the coefficient of the squared term: Divide each side by '-0.45'. -744.4444444 + 54.66666667x + x2 = 0 Move the constant term to the right: Add '744.4444444' to each side of the equation. -744.4444444 + 54.66666667x + 744.4444444 + x2 = 0 + 744.4444444 Reorder the terms: -744.4444444 + 744.4444444 + 54.66666667x + x2 = 0 + 744.4444444 Combine like terms: -744.4444444 + 744.4444444 = 0.0000000 0.0000000 + 54.66666667x + x2 = 0 + 744.4444444 54.66666667x + x2 = 0 + 744.4444444 Combine like terms: 0 + 744.4444444 = 744.4444444 54.66666667x + x2 = 744.4444444 The x term is 54.66666667x. Take half its coefficient (27.33333334). Square it (747.1111115) and add it to both sides. Add '747.1111115' to each side of the equation. 54.66666667x + 747.1111115 + x2 = 744.4444444 + 747.1111115 Reorder the terms: 747.1111115 + 54.66666667x + x2 = 744.4444444 + 747.1111115 Combine like terms: 744.4444444 + 747.1111115 = 1491.5555559 747.1111115 + 54.66666667x + x2 = 1491.5555559 Factor a perfect square on the left side: (x + 27.33333334)(x + 27.33333334) = 1491.5555559 Calculate the square root of the right side: 38.620662292 Break this problem into two subproblems by setting (x + 27.33333334) equal to 38.620662292 and -38.620662292.Subproblem 1
x + 27.33333334 = 38.620662292 Simplifying x + 27.33333334 = 38.620662292 Reorder the terms: 27.33333334 + x = 38.620662292 Solving 27.33333334 + x = 38.620662292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.33333334' to each side of the equation. 27.33333334 + -27.33333334 + x = 38.620662292 + -27.33333334 Combine like terms: 27.33333334 + -27.33333334 = 0.00000000 0.00000000 + x = 38.620662292 + -27.33333334 x = 38.620662292 + -27.33333334 Combine like terms: 38.620662292 + -27.33333334 = 11.287328952 x = 11.287328952 Simplifying x = 11.287328952Subproblem 2
x + 27.33333334 = -38.620662292 Simplifying x + 27.33333334 = -38.620662292 Reorder the terms: 27.33333334 + x = -38.620662292 Solving 27.33333334 + x = -38.620662292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.33333334' to each side of the equation. 27.33333334 + -27.33333334 + x = -38.620662292 + -27.33333334 Combine like terms: 27.33333334 + -27.33333334 = 0.00000000 0.00000000 + x = -38.620662292 + -27.33333334 x = -38.620662292 + -27.33333334 Combine like terms: -38.620662292 + -27.33333334 = -65.953995632 x = -65.953995632 Simplifying x = -65.953995632Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.287328952, -65.953995632}
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