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Simplifying 481 + -200x + 12x2 = 0 Solving 481 + -200x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 40.08333333 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '-40.08333333' to each side of the equation. 40.08333333 + -16.66666667x + -40.08333333 + x2 = 0 + -40.08333333 Reorder the terms: 40.08333333 + -40.08333333 + -16.66666667x + x2 = 0 + -40.08333333 Combine like terms: 40.08333333 + -40.08333333 = 0.00000000 0.00000000 + -16.66666667x + x2 = 0 + -40.08333333 -16.66666667x + x2 = 0 + -40.08333333 Combine like terms: 0 + -40.08333333 = -40.08333333 -16.66666667x + x2 = -40.08333333 The x term is -16.66666667x. Take half its coefficient (-8.333333335). Square it (69.44444447) and add it to both sides. Add '69.44444447' to each side of the equation. -16.66666667x + 69.44444447 + x2 = -40.08333333 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = -40.08333333 + 69.44444447 Combine like terms: -40.08333333 + 69.44444447 = 29.36111114 69.44444447 + -16.66666667x + x2 = 29.36111114 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 29.36111114 Calculate the square root of the right side: 5.418589405 Break this problem into two subproblems by setting (x + -8.333333335) equal to 5.418589405 and -5.418589405.Subproblem 1
x + -8.333333335 = 5.418589405 Simplifying x + -8.333333335 = 5.418589405 Reorder the terms: -8.333333335 + x = 5.418589405 Solving -8.333333335 + x = 5.418589405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = 5.418589405 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 5.418589405 + 8.333333335 x = 5.418589405 + 8.333333335 Combine like terms: 5.418589405 + 8.333333335 = 13.75192274 x = 13.75192274 Simplifying x = 13.75192274Subproblem 2
x + -8.333333335 = -5.418589405 Simplifying x + -8.333333335 = -5.418589405 Reorder the terms: -8.333333335 + x = -5.418589405 Solving -8.333333335 + x = -5.418589405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = -5.418589405 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -5.418589405 + 8.333333335 x = -5.418589405 + 8.333333335 Combine like terms: -5.418589405 + 8.333333335 = 2.91474393 x = 2.91474393 Simplifying x = 2.91474393Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.75192274, 2.91474393}
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