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Simplifying 3859 = -16x2 + 514x + 66 Reorder the terms: 3859 = 66 + 514x + -16x2 Solving 3859 = 66 + 514x + -16x2 Solving for variable 'x'. Combine like terms: 3859 + -66 = 3793 3793 + -514x + 16x2 = 66 + 514x + -16x2 + -66 + -514x + 16x2 Reorder the terms: 3793 + -514x + 16x2 = 66 + -66 + 514x + -514x + -16x2 + 16x2 Combine like terms: 66 + -66 = 0 3793 + -514x + 16x2 = 0 + 514x + -514x + -16x2 + 16x2 3793 + -514x + 16x2 = 514x + -514x + -16x2 + 16x2 Combine like terms: 514x + -514x = 0 3793 + -514x + 16x2 = 0 + -16x2 + 16x2 3793 + -514x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 3793 + -514x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 237.0625 + -32.125x + x2 = 0 Move the constant term to the right: Add '-237.0625' to each side of the equation. 237.0625 + -32.125x + -237.0625 + x2 = 0 + -237.0625 Reorder the terms: 237.0625 + -237.0625 + -32.125x + x2 = 0 + -237.0625 Combine like terms: 237.0625 + -237.0625 = 0.0000 0.0000 + -32.125x + x2 = 0 + -237.0625 -32.125x + x2 = 0 + -237.0625 Combine like terms: 0 + -237.0625 = -237.0625 -32.125x + x2 = -237.0625 The x term is -32.125x. Take half its coefficient (-16.0625). Square it (258.0039063) and add it to both sides. Add '258.0039063' to each side of the equation. -32.125x + 258.0039063 + x2 = -237.0625 + 258.0039063 Reorder the terms: 258.0039063 + -32.125x + x2 = -237.0625 + 258.0039063 Combine like terms: -237.0625 + 258.0039063 = 20.9414063 258.0039063 + -32.125x + x2 = 20.9414063 Factor a perfect square on the left side: (x + -16.0625)(x + -16.0625) = 20.9414063 Calculate the square root of the right side: 4.576178132 Break this problem into two subproblems by setting (x + -16.0625) equal to 4.576178132 and -4.576178132.Subproblem 1
x + -16.0625 = 4.576178132 Simplifying x + -16.0625 = 4.576178132 Reorder the terms: -16.0625 + x = 4.576178132 Solving -16.0625 + x = 4.576178132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.0625' to each side of the equation. -16.0625 + 16.0625 + x = 4.576178132 + 16.0625 Combine like terms: -16.0625 + 16.0625 = 0.0000 0.0000 + x = 4.576178132 + 16.0625 x = 4.576178132 + 16.0625 Combine like terms: 4.576178132 + 16.0625 = 20.638678132 x = 20.638678132 Simplifying x = 20.638678132Subproblem 2
x + -16.0625 = -4.576178132 Simplifying x + -16.0625 = -4.576178132 Reorder the terms: -16.0625 + x = -4.576178132 Solving -16.0625 + x = -4.576178132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.0625' to each side of the equation. -16.0625 + 16.0625 + x = -4.576178132 + 16.0625 Combine like terms: -16.0625 + 16.0625 = 0.0000 0.0000 + x = -4.576178132 + 16.0625 x = -4.576178132 + 16.0625 Combine like terms: -4.576178132 + 16.0625 = 11.486321868 x = 11.486321868 Simplifying x = 11.486321868Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.638678132, 11.486321868}
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