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Simplifying 0 = -16x2 + 200x + 6 Reorder the terms: 0 = 6 + 200x + -16x2 Solving 0 = 6 + 200x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -200x + 16x2 = 6 + 200x + -16x2 + -6 + -200x + 16x2 Reorder the terms: -6 + -200x + 16x2 = 6 + -6 + 200x + -200x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -6 + -200x + 16x2 = 0 + 200x + -200x + -16x2 + 16x2 -6 + -200x + 16x2 = 200x + -200x + -16x2 + 16x2 Combine like terms: 200x + -200x = 0 -6 + -200x + 16x2 = 0 + -16x2 + 16x2 -6 + -200x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -6 + -200x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -100x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -100x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -100x + 8x2 = 0 Solving -3 + -100x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -12.5x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -12.5x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -12.5x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -12.5x + x2 = 0 + 0.375 -12.5x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -12.5x + x2 = 0.375 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 0.375 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 0.375 + 39.0625 Combine like terms: 0.375 + 39.0625 = 39.4375 39.0625 + -12.5x + x2 = 39.4375 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 39.4375 Calculate the square root of the right side: 6.279928344 Break this problem into two subproblems by setting (x + -6.25) equal to 6.279928344 and -6.279928344.Subproblem 1
x + -6.25 = 6.279928344 Simplifying x + -6.25 = 6.279928344 Reorder the terms: -6.25 + x = 6.279928344 Solving -6.25 + x = 6.279928344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 6.279928344 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.279928344 + 6.25 x = 6.279928344 + 6.25 Combine like terms: 6.279928344 + 6.25 = 12.529928344 x = 12.529928344 Simplifying x = 12.529928344Subproblem 2
x + -6.25 = -6.279928344 Simplifying x + -6.25 = -6.279928344 Reorder the terms: -6.25 + x = -6.279928344 Solving -6.25 + x = -6.279928344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -6.279928344 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.279928344 + 6.25 x = -6.279928344 + 6.25 Combine like terms: -6.279928344 + 6.25 = -0.029928344 x = -0.029928344 Simplifying x = -0.029928344Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.529928344, -0.029928344}Solution
x = {12.529928344, -0.029928344}
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