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Simplifying 5000 = 16x2 + -4886 + -10x Reorder the terms: 5000 = -4886 + -10x + 16x2 Solving 5000 = -4886 + -10x + 16x2 Solving for variable 'x'. Combine like terms: 5000 + 4886 = 9886 9886 + 10x + -16x2 = -4886 + -10x + 16x2 + 4886 + 10x + -16x2 Reorder the terms: 9886 + 10x + -16x2 = -4886 + 4886 + -10x + 10x + 16x2 + -16x2 Combine like terms: -4886 + 4886 = 0 9886 + 10x + -16x2 = 0 + -10x + 10x + 16x2 + -16x2 9886 + 10x + -16x2 = -10x + 10x + 16x2 + -16x2 Combine like terms: -10x + 10x = 0 9886 + 10x + -16x2 = 0 + 16x2 + -16x2 9886 + 10x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 9886 + 10x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4943 + 5x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4943 + 5x + -8x2)' equal to zero and attempt to solve: Simplifying 4943 + 5x + -8x2 = 0 Solving 4943 + 5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -617.875 + -0.625x + x2 = 0 Move the constant term to the right: Add '617.875' to each side of the equation. -617.875 + -0.625x + 617.875 + x2 = 0 + 617.875 Reorder the terms: -617.875 + 617.875 + -0.625x + x2 = 0 + 617.875 Combine like terms: -617.875 + 617.875 = 0.000 0.000 + -0.625x + x2 = 0 + 617.875 -0.625x + x2 = 0 + 617.875 Combine like terms: 0 + 617.875 = 617.875 -0.625x + x2 = 617.875 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 617.875 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 617.875 + 0.09765625 Combine like terms: 617.875 + 0.09765625 = 617.97265625 0.09765625 + -0.625x + x2 = 617.97265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 617.97265625 Calculate the square root of the right side: 24.85905582 Break this problem into two subproblems by setting (x + -0.3125) equal to 24.85905582 and -24.85905582.Subproblem 1
x + -0.3125 = 24.85905582 Simplifying x + -0.3125 = 24.85905582 Reorder the terms: -0.3125 + x = 24.85905582 Solving -0.3125 + x = 24.85905582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 24.85905582 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 24.85905582 + 0.3125 x = 24.85905582 + 0.3125 Combine like terms: 24.85905582 + 0.3125 = 25.17155582 x = 25.17155582 Simplifying x = 25.17155582Subproblem 2
x + -0.3125 = -24.85905582 Simplifying x + -0.3125 = -24.85905582 Reorder the terms: -0.3125 + x = -24.85905582 Solving -0.3125 + x = -24.85905582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -24.85905582 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -24.85905582 + 0.3125 x = -24.85905582 + 0.3125 Combine like terms: -24.85905582 + 0.3125 = -24.54655582 x = -24.54655582 Simplifying x = -24.54655582Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.17155582, -24.54655582}Solution
x = {25.17155582, -24.54655582}
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