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Simplifying 4000 = -2x2 + 200x Reorder the terms: 4000 = 200x + -2x2 Solving 4000 = 200x + -2x2 Solving for variable 'x'. Reorder the terms: 4000 + -200x + 2x2 = 200x + -200x + -2x2 + 2x2 Combine like terms: 200x + -200x = 0 4000 + -200x + 2x2 = 0 + -2x2 + 2x2 4000 + -200x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 4000 + -200x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2000 + -100x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2000 + -100x + x2)' equal to zero and attempt to solve: Simplifying 2000 + -100x + x2 = 0 Solving 2000 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2000' to each side of the equation. 2000 + -100x + -2000 + x2 = 0 + -2000 Reorder the terms: 2000 + -2000 + -100x + x2 = 0 + -2000 Combine like terms: 2000 + -2000 = 0 0 + -100x + x2 = 0 + -2000 -100x + x2 = 0 + -2000 Combine like terms: 0 + -2000 = -2000 -100x + x2 = -2000 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -2000 + 2500 Reorder the terms: 2500 + -100x + x2 = -2000 + 2500 Combine like terms: -2000 + 2500 = 500 2500 + -100x + x2 = 500 Factor a perfect square on the left side: (x + -50)(x + -50) = 500 Calculate the square root of the right side: 22.360679775 Break this problem into two subproblems by setting (x + -50) equal to 22.360679775 and -22.360679775.Subproblem 1
x + -50 = 22.360679775 Simplifying x + -50 = 22.360679775 Reorder the terms: -50 + x = 22.360679775 Solving -50 + x = 22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 22.360679775 + 50 Combine like terms: -50 + 50 = 0 0 + x = 22.360679775 + 50 x = 22.360679775 + 50 Combine like terms: 22.360679775 + 50 = 72.360679775 x = 72.360679775 Simplifying x = 72.360679775Subproblem 2
x + -50 = -22.360679775 Simplifying x + -50 = -22.360679775 Reorder the terms: -50 + x = -22.360679775 Solving -50 + x = -22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -22.360679775 + 50 Combine like terms: -50 + 50 = 0 0 + x = -22.360679775 + 50 x = -22.360679775 + 50 Combine like terms: -22.360679775 + 50 = 27.639320225 x = 27.639320225 Simplifying x = 27.639320225Solution
The solution to the problem is based on the solutions from the subproblems. x = {72.360679775, 27.639320225}Solution
x = {72.360679775, 27.639320225}
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