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Simplifying 4000 = 2x2 + 2x Reorder the terms: 4000 = 2x + 2x2 Solving 4000 = 2x + 2x2 Solving for variable 'x'. Reorder the terms: 4000 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 4000 + -2x + -2x2 = 0 + 2x2 + -2x2 4000 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 4000 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2000 + -1x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2000 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 2000 + -1x + -1x2 = 0 Solving 2000 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2000 + x + x2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + x + x2 = 0 + 2000 x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 x + x2 = 2000 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 = 2000 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2000 + 0.25 Combine like terms: 2000 + 0.25 = 2000.25 1.25 + x2 = 2000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2000.25 Calculate the square root of the right side: 44.724154548 Break this problem into two subproblems by setting (x + 0.5) equal to 44.724154548 and -44.724154548.Subproblem 1
x + 0.5 = 44.724154548 Simplifying x + 0.5 = 44.724154548 Reorder the terms: 0.5 + x = 44.724154548 Solving 0.5 + x = 44.724154548 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 = 44.724154548 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 44.724154548 + -0.5 x = 44.724154548 + -0.5 Combine like terms: 44.724154548 + -0.5 = 44.224154548 x = 44.224154548 Simplifying x = 44.224154548Subproblem 2
x + 0.5 = -44.724154548 Simplifying x + 0.5 = -44.724154548 Reorder the terms: 0.5 + x = -44.724154548 Solving 0.5 + x = -44.724154548 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 = -44.724154548 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -44.724154548 + -0.5 x = -44.724154548 + -0.5 Combine like terms: -44.724154548 + -0.5 = -45.224154548 x = -45.224154548 Simplifying x = -45.224154548Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.224154548, -45.224154548}Solution
x = {44.224154548, -45.224154548}
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