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Simplifying 16 = -16x2 + 66x + 14 Reorder the terms: 16 = 14 + 66x + -16x2 Solving 16 = 14 + 66x + -16x2 Solving for variable 'x'. Combine like terms: 16 + -14 = 2 2 + -66x + 16x2 = 14 + 66x + -16x2 + -14 + -66x + 16x2 Reorder the terms: 2 + -66x + 16x2 = 14 + -14 + 66x + -66x + -16x2 + 16x2 Combine like terms: 14 + -14 = 0 2 + -66x + 16x2 = 0 + 66x + -66x + -16x2 + 16x2 2 + -66x + 16x2 = 66x + -66x + -16x2 + 16x2 Combine like terms: 66x + -66x = 0 2 + -66x + 16x2 = 0 + -16x2 + 16x2 2 + -66x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 2 + -66x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -33x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -33x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + -33x + 8x2 = 0 Solving 1 + -33x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -4.125x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -4.125x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -4.125x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -4.125x + x2 = 0 + -0.125 -4.125x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -4.125x + x2 = -0.125 The x term is -4.125x. Take half its coefficient (-2.0625). Square it (4.25390625) and add it to both sides. Add '4.25390625' to each side of the equation. -4.125x + 4.25390625 + x2 = -0.125 + 4.25390625 Reorder the terms: 4.25390625 + -4.125x + x2 = -0.125 + 4.25390625 Combine like terms: -0.125 + 4.25390625 = 4.12890625 4.25390625 + -4.125x + x2 = 4.12890625 Factor a perfect square on the left side: (x + -2.0625)(x + -2.0625) = 4.12890625 Calculate the square root of the right side: 2.031971026 Break this problem into two subproblems by setting (x + -2.0625) equal to 2.031971026 and -2.031971026.Subproblem 1
x + -2.0625 = 2.031971026 Simplifying x + -2.0625 = 2.031971026 Reorder the terms: -2.0625 + x = 2.031971026 Solving -2.0625 + x = 2.031971026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = 2.031971026 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = 2.031971026 + 2.0625 x = 2.031971026 + 2.0625 Combine like terms: 2.031971026 + 2.0625 = 4.094471026 x = 4.094471026 Simplifying x = 4.094471026Subproblem 2
x + -2.0625 = -2.031971026 Simplifying x + -2.0625 = -2.031971026 Reorder the terms: -2.0625 + x = -2.031971026 Solving -2.0625 + x = -2.031971026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = -2.031971026 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = -2.031971026 + 2.0625 x = -2.031971026 + 2.0625 Combine like terms: -2.031971026 + 2.0625 = 0.030528974 x = 0.030528974 Simplifying x = 0.030528974Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.094471026, 0.030528974}Solution
x = {4.094471026, 0.030528974}
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