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Simplifying -301000x2 + -301000x + 635000 = 0 Reorder the terms: 635000 + -301000x + -301000x2 = 0 Solving 635000 + -301000x + -301000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '1000'. 1000(635 + -301x + -301x2) = 0 Ignore the factor 1000.Subproblem 1
Set the factor '(635 + -301x + -301x2)' equal to zero and attempt to solve: Simplifying 635 + -301x + -301x2 = 0 Solving 635 + -301x + -301x2 = 0 Begin completing the square. Divide all terms by -301 the coefficient of the squared term: Divide each side by '-301'. -2.109634551 + x + x2 = 0 Move the constant term to the right: Add '2.109634551' to each side of the equation. -2.109634551 + x + 2.109634551 + x2 = 0 + 2.109634551 Reorder the terms: -2.109634551 + 2.109634551 + x + x2 = 0 + 2.109634551 Combine like terms: -2.109634551 + 2.109634551 = 0.000000000 0.000000000 + x + x2 = 0 + 2.109634551 x + x2 = 0 + 2.109634551 Combine like terms: 0 + 2.109634551 = 2.109634551 x + x2 = 2.109634551 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 2.109634551 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.109634551 + 0.25 Combine like terms: 2.109634551 + 0.25 = 2.359634551 1.25 + x2 = 2.359634551 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.359634551 Calculate the square root of the right side: 1.536110201 Break this problem into two subproblems by setting (x + 0.5) equal to 1.536110201 and -1.536110201.Subproblem 1
x + 0.5 = 1.536110201 Simplifying x + 0.5 = 1.536110201 Reorder the terms: 0.5 + x = 1.536110201 Solving 0.5 + x = 1.536110201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.536110201 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.536110201 + -0.5 x = 1.536110201 + -0.5 Combine like terms: 1.536110201 + -0.5 = 1.036110201 x = 1.036110201 Simplifying x = 1.036110201Subproblem 2
x + 0.5 = -1.536110201 Simplifying x + 0.5 = -1.536110201 Reorder the terms: 0.5 + x = -1.536110201 Solving 0.5 + x = -1.536110201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.536110201 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.536110201 + -0.5 x = -1.536110201 + -0.5 Combine like terms: -1.536110201 + -0.5 = -2.036110201 x = -2.036110201 Simplifying x = -2.036110201Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.036110201, -2.036110201}Solution
x = {1.036110201, -2.036110201}
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