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Simplifying 0 = -50x2 + 1000x + -2000 Reorder the terms: 0 = -2000 + 1000x + -50x2 Solving 0 = -2000 + 1000x + -50x2 Solving for variable 'x'. Combine like terms: 0 + 2000 = 2000 2000 + -1000x + 50x2 = -2000 + 1000x + -50x2 + 2000 + -1000x + 50x2 Reorder the terms: 2000 + -1000x + 50x2 = -2000 + 2000 + 1000x + -1000x + -50x2 + 50x2 Combine like terms: -2000 + 2000 = 0 2000 + -1000x + 50x2 = 0 + 1000x + -1000x + -50x2 + 50x2 2000 + -1000x + 50x2 = 1000x + -1000x + -50x2 + 50x2 Combine like terms: 1000x + -1000x = 0 2000 + -1000x + 50x2 = 0 + -50x2 + 50x2 2000 + -1000x + 50x2 = -50x2 + 50x2 Combine like terms: -50x2 + 50x2 = 0 2000 + -1000x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '50'. 50(40 + -20x + x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(40 + -20x + x2)' equal to zero and attempt to solve: Simplifying 40 + -20x + x2 = 0 Solving 40 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -20x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -20x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -20x + x2 = 0 + -40 -20x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -20x + x2 = -40 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -40 + 100 Reorder the terms: 100 + -20x + x2 = -40 + 100 Combine like terms: -40 + 100 = 60 100 + -20x + x2 = 60 Factor a perfect square on the left side: (x + -10)(x + -10) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -10) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -10 = 7.745966692 Simplifying x + -10 = 7.745966692 Reorder the terms: -10 + x = 7.745966692 Solving -10 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 7.745966692 + 10 Combine like terms: -10 + 10 = 0 0 + x = 7.745966692 + 10 x = 7.745966692 + 10 Combine like terms: 7.745966692 + 10 = 17.745966692 x = 17.745966692 Simplifying x = 17.745966692Subproblem 2
x + -10 = -7.745966692 Simplifying x + -10 = -7.745966692 Reorder the terms: -10 + x = -7.745966692 Solving -10 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -7.745966692 + 10 Combine like terms: -10 + 10 = 0 0 + x = -7.745966692 + 10 x = -7.745966692 + 10 Combine like terms: -7.745966692 + 10 = 2.254033308 x = 2.254033308 Simplifying x = 2.254033308Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.745966692, 2.254033308}Solution
x = {17.745966692, 2.254033308}
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