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Simplifying 0 = 0.4375 + -3.5x + 6x2 Solving 0 = 0.4375 + -3.5x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -0.4375 = -0.4375 -0.4375 + 3.5x + -6x2 = 0.4375 + -3.5x + 6x2 + -0.4375 + 3.5x + -6x2 Reorder the terms: -0.4375 + 3.5x + -6x2 = 0.4375 + -0.4375 + -3.5x + 3.5x + 6x2 + -6x2 Combine like terms: 0.4375 + -0.4375 = 0.0000 -0.4375 + 3.5x + -6x2 = 0.0000 + -3.5x + 3.5x + 6x2 + -6x2 -0.4375 + 3.5x + -6x2 = -3.5x + 3.5x + 6x2 + -6x2 Combine like terms: -3.5x + 3.5x = 0.0 -0.4375 + 3.5x + -6x2 = 0.0 + 6x2 + -6x2 -0.4375 + 3.5x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -0.4375 + 3.5x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.07291666667 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '-0.07291666667' to each side of the equation. 0.07291666667 + -0.5833333333x + -0.07291666667 + x2 = 0 + -0.07291666667 Reorder the terms: 0.07291666667 + -0.07291666667 + -0.5833333333x + x2 = 0 + -0.07291666667 Combine like terms: 0.07291666667 + -0.07291666667 = 0.00000000000 0.00000000000 + -0.5833333333x + x2 = 0 + -0.07291666667 -0.5833333333x + x2 = 0 + -0.07291666667 Combine like terms: 0 + -0.07291666667 = -0.07291666667 -0.5833333333x + x2 = -0.07291666667 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = -0.07291666667 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = -0.07291666667 + 0.08506944446 Combine like terms: -0.07291666667 + 0.08506944446 = 0.01215277779 0.08506944446 + -0.5833333333x + x2 = 0.01215277779 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 0.01215277779 Calculate the square root of the right side: 0.110239638 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 0.110239638 and -0.110239638.Subproblem 1
x + -0.2916666667 = 0.110239638 Simplifying x + -0.2916666667 = 0.110239638 Reorder the terms: -0.2916666667 + x = 0.110239638 Solving -0.2916666667 + x = 0.110239638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 0.110239638 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 0.110239638 + 0.2916666667 x = 0.110239638 + 0.2916666667 Combine like terms: 0.110239638 + 0.2916666667 = 0.4019063047 x = 0.4019063047 Simplifying x = 0.4019063047Subproblem 2
x + -0.2916666667 = -0.110239638 Simplifying x + -0.2916666667 = -0.110239638 Reorder the terms: -0.2916666667 + x = -0.110239638 Solving -0.2916666667 + x = -0.110239638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -0.110239638 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -0.110239638 + 0.2916666667 x = -0.110239638 + 0.2916666667 Combine like terms: -0.110239638 + 0.2916666667 = 0.1814270287 x = 0.1814270287 Simplifying x = 0.1814270287Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4019063047, 0.1814270287}
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