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Simplifying 5000 = 16x2 + -4686 + -10x Reorder the terms: 5000 = -4686 + -10x + 16x2 Solving 5000 = -4686 + -10x + 16x2 Solving for variable 'x'. Combine like terms: 5000 + 4686 = 9686 9686 + 10x + -16x2 = -4686 + -10x + 16x2 + 4686 + 10x + -16x2 Reorder the terms: 9686 + 10x + -16x2 = -4686 + 4686 + -10x + 10x + 16x2 + -16x2 Combine like terms: -4686 + 4686 = 0 9686 + 10x + -16x2 = 0 + -10x + 10x + 16x2 + -16x2 9686 + 10x + -16x2 = -10x + 10x + 16x2 + -16x2 Combine like terms: -10x + 10x = 0 9686 + 10x + -16x2 = 0 + 16x2 + -16x2 9686 + 10x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 9686 + 10x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4843 + 5x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4843 + 5x + -8x2)' equal to zero and attempt to solve: Simplifying 4843 + 5x + -8x2 = 0 Solving 4843 + 5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -605.375 + -0.625x + x2 = 0 Move the constant term to the right: Add '605.375' to each side of the equation. -605.375 + -0.625x + 605.375 + x2 = 0 + 605.375 Reorder the terms: -605.375 + 605.375 + -0.625x + x2 = 0 + 605.375 Combine like terms: -605.375 + 605.375 = 0.000 0.000 + -0.625x + x2 = 0 + 605.375 -0.625x + x2 = 0 + 605.375 Combine like terms: 0 + 605.375 = 605.375 -0.625x + x2 = 605.375 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 = 605.375 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 605.375 + 0.09765625 Combine like terms: 605.375 + 0.09765625 = 605.47265625 0.09765625 + -0.625x + x2 = 605.47265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 605.47265625 Calculate the square root of the right side: 24.606353981 Break this problem into two subproblems by setting (x + -0.3125) equal to 24.606353981 and -24.606353981.Subproblem 1
x + -0.3125 = 24.606353981 Simplifying x + -0.3125 = 24.606353981 Reorder the terms: -0.3125 + x = 24.606353981 Solving -0.3125 + x = 24.606353981 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 = 24.606353981 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 24.606353981 + 0.3125 x = 24.606353981 + 0.3125 Combine like terms: 24.606353981 + 0.3125 = 24.918853981 x = 24.918853981 Simplifying x = 24.918853981Subproblem 2
x + -0.3125 = -24.606353981 Simplifying x + -0.3125 = -24.606353981 Reorder the terms: -0.3125 + x = -24.606353981 Solving -0.3125 + x = -24.606353981 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 = -24.606353981 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -24.606353981 + 0.3125 x = -24.606353981 + 0.3125 Combine like terms: -24.606353981 + 0.3125 = -24.293853981 x = -24.293853981 Simplifying x = -24.293853981Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.918853981, -24.293853981}Solution
x = {24.918853981, -24.293853981}
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