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Simplifying 46.2x2 + -251.2x + 0.4995 = 0 Reorder the terms: 0.4995 + -251.2x + 46.2x2 = 0 Solving 0.4995 + -251.2x + 46.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 46.2 the coefficient of the squared term: Divide each side by '46.2'. 0.01081168831 + -5.437229437x + x2 = 0 Move the constant term to the right: Add '-0.01081168831' to each side of the equation. 0.01081168831 + -5.437229437x + -0.01081168831 + x2 = 0 + -0.01081168831 Reorder the terms: 0.01081168831 + -0.01081168831 + -5.437229437x + x2 = 0 + -0.01081168831 Combine like terms: 0.01081168831 + -0.01081168831 = 0.00000000000 0.00000000000 + -5.437229437x + x2 = 0 + -0.01081168831 -5.437229437x + x2 = 0 + -0.01081168831 Combine like terms: 0 + -0.01081168831 = -0.01081168831 -5.437229437x + x2 = -0.01081168831 The x term is -5.437229437x. Take half its coefficient (-2.718614719). Square it (7.390865990) and add it to both sides. Add '7.390865990' to each side of the equation. -5.437229437x + 7.390865990 + x2 = -0.01081168831 + 7.390865990 Reorder the terms: 7.390865990 + -5.437229437x + x2 = -0.01081168831 + 7.390865990 Combine like terms: -0.01081168831 + 7.390865990 = 7.38005430169 7.390865990 + -5.437229437x + x2 = 7.38005430169 Factor a perfect square on the left side: (x + -2.718614719)(x + -2.718614719) = 7.38005430169 Calculate the square root of the right side: 2.716625536 Break this problem into two subproblems by setting (x + -2.718614719) equal to 2.716625536 and -2.716625536.Subproblem 1
x + -2.718614719 = 2.716625536 Simplifying x + -2.718614719 = 2.716625536 Reorder the terms: -2.718614719 + x = 2.716625536 Solving -2.718614719 + x = 2.716625536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.718614719' to each side of the equation. -2.718614719 + 2.718614719 + x = 2.716625536 + 2.718614719 Combine like terms: -2.718614719 + 2.718614719 = 0.000000000 0.000000000 + x = 2.716625536 + 2.718614719 x = 2.716625536 + 2.718614719 Combine like terms: 2.716625536 + 2.718614719 = 5.435240255 x = 5.435240255 Simplifying x = 5.435240255Subproblem 2
x + -2.718614719 = -2.716625536 Simplifying x + -2.718614719 = -2.716625536 Reorder the terms: -2.718614719 + x = -2.716625536 Solving -2.718614719 + x = -2.716625536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.718614719' to each side of the equation. -2.718614719 + 2.718614719 + x = -2.716625536 + 2.718614719 Combine like terms: -2.718614719 + 2.718614719 = 0.000000000 0.000000000 + x = -2.716625536 + 2.718614719 x = -2.716625536 + 2.718614719 Combine like terms: -2.716625536 + 2.718614719 = 0.001989183 x = 0.001989183 Simplifying x = 0.001989183Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.435240255, 0.001989183}
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