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Simplifying 2x2 + -10000x + -5 = 0 Reorder the terms: -5 + -10000x + 2x2 = 0 Solving -5 + -10000x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -5000x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -5000x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -5000x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -5000x + x2 = 0 + 2.5 -5000x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -5000x + x2 = 2.5 The x term is -5000x. Take half its coefficient (-2500). Square it (6250000) and add it to both sides. Add '6250000' to each side of the equation. -5000x + 6250000 + x2 = 2.5 + 6250000 Reorder the terms: 6250000 + -5000x + x2 = 2.5 + 6250000 Combine like terms: 2.5 + 6250000 = 6250002.5 6250000 + -5000x + x2 = 6250002.5 Factor a perfect square on the left side: (x + -2500)(x + -2500) = 6250002.5 Calculate the square root of the right side: 2500.0005 Break this problem into two subproblems by setting (x + -2500) equal to 2500.0005 and -2500.0005.Subproblem 1
x + -2500 = 2500.0005 Simplifying x + -2500 = 2500.0005 Reorder the terms: -2500 + x = 2500.0005 Solving -2500 + x = 2500.0005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2500' to each side of the equation. -2500 + 2500 + x = 2500.0005 + 2500 Combine like terms: -2500 + 2500 = 0 0 + x = 2500.0005 + 2500 x = 2500.0005 + 2500 Combine like terms: 2500.0005 + 2500 = 5000.0005 x = 5000.0005 Simplifying x = 5000.0005Subproblem 2
x + -2500 = -2500.0005 Simplifying x + -2500 = -2500.0005 Reorder the terms: -2500 + x = -2500.0005 Solving -2500 + x = -2500.0005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2500' to each side of the equation. -2500 + 2500 + x = -2500.0005 + 2500 Combine like terms: -2500 + 2500 = 0 0 + x = -2500.0005 + 2500 x = -2500.0005 + 2500 Combine like terms: -2500.0005 + 2500 = -0.0005 x = -0.0005 Simplifying x = -0.0005Solution
The solution to the problem is based on the solutions from the subproblems. x = {5000.0005, -0.0005}
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