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Simplifying 7000 = 3535x + -35x2 Solving 7000 = 3535x + -35x2 Solving for variable 'x'. Reorder the terms: 7000 + -3535x + 35x2 = 3535x + -3535x + -35x2 + 35x2 Combine like terms: 3535x + -3535x = 0 7000 + -3535x + 35x2 = 0 + -35x2 + 35x2 7000 + -3535x + 35x2 = -35x2 + 35x2 Combine like terms: -35x2 + 35x2 = 0 7000 + -3535x + 35x2 = 0 Factor out the Greatest Common Factor (GCF), '35'. 35(200 + -101x + x2) = 0 Ignore the factor 35.Subproblem 1
Set the factor '(200 + -101x + x2)' equal to zero and attempt to solve: Simplifying 200 + -101x + x2 = 0 Solving 200 + -101x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -101x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -101x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -101x + x2 = 0 + -200 -101x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -101x + x2 = -200 The x term is -101x. Take half its coefficient (-50.5). Square it (2550.25) and add it to both sides. Add '2550.25' to each side of the equation. -101x + 2550.25 + x2 = -200 + 2550.25 Reorder the terms: 2550.25 + -101x + x2 = -200 + 2550.25 Combine like terms: -200 + 2550.25 = 2350.25 2550.25 + -101x + x2 = 2350.25 Factor a perfect square on the left side: (x + -50.5)(x + -50.5) = 2350.25 Calculate the square root of the right side: 48.479377059 Break this problem into two subproblems by setting (x + -50.5) equal to 48.479377059 and -48.479377059.Subproblem 1
x + -50.5 = 48.479377059 Simplifying x + -50.5 = 48.479377059 Reorder the terms: -50.5 + x = 48.479377059 Solving -50.5 + x = 48.479377059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50.5' to each side of the equation. -50.5 + 50.5 + x = 48.479377059 + 50.5 Combine like terms: -50.5 + 50.5 = 0.0 0.0 + x = 48.479377059 + 50.5 x = 48.479377059 + 50.5 Combine like terms: 48.479377059 + 50.5 = 98.979377059 x = 98.979377059 Simplifying x = 98.979377059Subproblem 2
x + -50.5 = -48.479377059 Simplifying x + -50.5 = -48.479377059 Reorder the terms: -50.5 + x = -48.479377059 Solving -50.5 + x = -48.479377059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50.5' to each side of the equation. -50.5 + 50.5 + x = -48.479377059 + 50.5 Combine like terms: -50.5 + 50.5 = 0.0 0.0 + x = -48.479377059 + 50.5 x = -48.479377059 + 50.5 Combine like terms: -48.479377059 + 50.5 = 2.020622941 x = 2.020622941 Simplifying x = 2.020622941Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.979377059, 2.020622941}Solution
x = {98.979377059, 2.020622941}
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