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Simplifying 0 = -16x2 + 200x + 133 Reorder the terms: 0 = 133 + 200x + -16x2 Solving 0 = 133 + 200x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -133 = -133 -133 + -200x + 16x2 = 133 + 200x + -16x2 + -133 + -200x + 16x2 Reorder the terms: -133 + -200x + 16x2 = 133 + -133 + 200x + -200x + -16x2 + 16x2 Combine like terms: 133 + -133 = 0 -133 + -200x + 16x2 = 0 + 200x + -200x + -16x2 + 16x2 -133 + -200x + 16x2 = 200x + -200x + -16x2 + 16x2 Combine like terms: 200x + -200x = 0 -133 + -200x + 16x2 = 0 + -16x2 + 16x2 -133 + -200x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -133 + -200x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -8.3125 + -12.5x + x2 = 0 Move the constant term to the right: Add '8.3125' to each side of the equation. -8.3125 + -12.5x + 8.3125 + x2 = 0 + 8.3125 Reorder the terms: -8.3125 + 8.3125 + -12.5x + x2 = 0 + 8.3125 Combine like terms: -8.3125 + 8.3125 = 0.0000 0.0000 + -12.5x + x2 = 0 + 8.3125 -12.5x + x2 = 0 + 8.3125 Combine like terms: 0 + 8.3125 = 8.3125 -12.5x + x2 = 8.3125 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 8.3125 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 8.3125 + 39.0625 Combine like terms: 8.3125 + 39.0625 = 47.375 39.0625 + -12.5x + x2 = 47.375 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 47.375 Calculate the square root of the right side: 6.882949949 Break this problem into two subproblems by setting (x + -6.25) equal to 6.882949949 and -6.882949949.Subproblem 1
x + -6.25 = 6.882949949 Simplifying x + -6.25 = 6.882949949 Reorder the terms: -6.25 + x = 6.882949949 Solving -6.25 + x = 6.882949949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 6.882949949 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.882949949 + 6.25 x = 6.882949949 + 6.25 Combine like terms: 6.882949949 + 6.25 = 13.132949949 x = 13.132949949 Simplifying x = 13.132949949Subproblem 2
x + -6.25 = -6.882949949 Simplifying x + -6.25 = -6.882949949 Reorder the terms: -6.25 + x = -6.882949949 Solving -6.25 + x = -6.882949949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -6.882949949 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.882949949 + 6.25 x = -6.882949949 + 6.25 Combine like terms: -6.882949949 + 6.25 = -0.632949949 x = -0.632949949 Simplifying x = -0.632949949Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.132949949, -0.632949949}
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