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Simplifying (x) = -16x2 + 500 x = -16x2 + 500 Reorder the terms: x = 500 + -16x2 Solving x = 500 + -16x2 Solving for variable 'x'. Reorder the terms: -500 + x + 16x2 = 500 + -16x2 + -500 + 16x2 Reorder the terms: -500 + x + 16x2 = 500 + -500 + -16x2 + 16x2 Combine like terms: 500 + -500 = 0 -500 + x + 16x2 = 0 + -16x2 + 16x2 -500 + x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -500 + x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -31.25 + 0.0625x + x2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + 0.0625x + 31.25 + x2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + 0.0625x + x2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + 0.0625x + x2 = 0 + 31.25 0.0625x + x2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 0.0625x + x2 = 31.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.0625x + 0.25 + x2 = 31.25 + 0.25 Reorder the terms: 0.25 + 0.0625x + x2 = 31.25 + 0.25 Combine like terms: 31.25 + 0.25 = 31.5 0.25 + 0.0625x + x2 = 31.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 31.5 Calculate the square root of the right side: 5.61248608 Break this problem into two subproblems by setting (x + 0.5) equal to 5.61248608 and -5.61248608.Subproblem 1
x + 0.5 = 5.61248608 Simplifying x + 0.5 = 5.61248608 Reorder the terms: 0.5 + x = 5.61248608 Solving 0.5 + x = 5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.61248608 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.61248608 + -0.5 x = 5.61248608 + -0.5 Combine like terms: 5.61248608 + -0.5 = 5.11248608 x = 5.11248608 Simplifying x = 5.11248608Subproblem 2
x + 0.5 = -5.61248608 Simplifying x + 0.5 = -5.61248608 Reorder the terms: 0.5 + x = -5.61248608 Solving 0.5 + x = -5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.61248608 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.61248608 + -0.5 x = -5.61248608 + -0.5 Combine like terms: -5.61248608 + -0.5 = -6.11248608 x = -6.11248608 Simplifying x = -6.11248608Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.11248608, -6.11248608}
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