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Simplifying x = 200x + -2x2 + -1x2 + 20x + 7875 Reorder the terms: x = 7875 + 200x + 20x + -2x2 + -1x2 Combine like terms: 200x + 20x = 220x x = 7875 + 220x + -2x2 + -1x2 Combine like terms: -2x2 + -1x2 = -3x2 x = 7875 + 220x + -3x2 Solving x = 7875 + 220x + -3x2 Solving for variable 'x'. Reorder the terms: -7875 + x + -220x + 3x2 = 7875 + 220x + -3x2 + -7875 + -220x + 3x2 Combine like terms: x + -220x = -219x -7875 + -219x + 3x2 = 7875 + 220x + -3x2 + -7875 + -220x + 3x2 Reorder the terms: -7875 + -219x + 3x2 = 7875 + -7875 + 220x + -220x + -3x2 + 3x2 Combine like terms: 7875 + -7875 = 0 -7875 + -219x + 3x2 = 0 + 220x + -220x + -3x2 + 3x2 -7875 + -219x + 3x2 = 220x + -220x + -3x2 + 3x2 Combine like terms: 220x + -220x = 0 -7875 + -219x + 3x2 = 0 + -3x2 + 3x2 -7875 + -219x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -7875 + -219x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2625 + -73x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2625 + -73x + x2)' equal to zero and attempt to solve: Simplifying -2625 + -73x + x2 = 0 Solving -2625 + -73x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2625' to each side of the equation. -2625 + -73x + 2625 + x2 = 0 + 2625 Reorder the terms: -2625 + 2625 + -73x + x2 = 0 + 2625 Combine like terms: -2625 + 2625 = 0 0 + -73x + x2 = 0 + 2625 -73x + x2 = 0 + 2625 Combine like terms: 0 + 2625 = 2625 -73x + x2 = 2625 The x term is -73x. Take half its coefficient (-36.5). Square it (1332.25) and add it to both sides. Add '1332.25' to each side of the equation. -73x + 1332.25 + x2 = 2625 + 1332.25 Reorder the terms: 1332.25 + -73x + x2 = 2625 + 1332.25 Combine like terms: 2625 + 1332.25 = 3957.25 1332.25 + -73x + x2 = 3957.25 Factor a perfect square on the left side: (x + -36.5)(x + -36.5) = 3957.25 Calculate the square root of the right side: 62.906676911 Break this problem into two subproblems by setting (x + -36.5) equal to 62.906676911 and -62.906676911.Subproblem 1
x + -36.5 = 62.906676911 Simplifying x + -36.5 = 62.906676911 Reorder the terms: -36.5 + x = 62.906676911 Solving -36.5 + x = 62.906676911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.5' to each side of the equation. -36.5 + 36.5 + x = 62.906676911 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + x = 62.906676911 + 36.5 x = 62.906676911 + 36.5 Combine like terms: 62.906676911 + 36.5 = 99.406676911 x = 99.406676911 Simplifying x = 99.406676911Subproblem 2
x + -36.5 = -62.906676911 Simplifying x + -36.5 = -62.906676911 Reorder the terms: -36.5 + x = -62.906676911 Solving -36.5 + x = -62.906676911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.5' to each side of the equation. -36.5 + 36.5 + x = -62.906676911 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + x = -62.906676911 + 36.5 x = -62.906676911 + 36.5 Combine like terms: -62.906676911 + 36.5 = -26.406676911 x = -26.406676911 Simplifying x = -26.406676911Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.406676911, -26.406676911}Solution
x = {99.406676911, -26.406676911}
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