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Simplifying 9x2 + 100x + -2965550 = 0 Reorder the terms: -2965550 + 100x + 9x2 = 0 Solving -2965550 + 100x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -329505.5556 + 11.11111111x + x2 = 0 Move the constant term to the right: Add '329505.5556' to each side of the equation. -329505.5556 + 11.11111111x + 329505.5556 + x2 = 0 + 329505.5556 Reorder the terms: -329505.5556 + 329505.5556 + 11.11111111x + x2 = 0 + 329505.5556 Combine like terms: -329505.5556 + 329505.5556 = 0.0000 0.0000 + 11.11111111x + x2 = 0 + 329505.5556 11.11111111x + x2 = 0 + 329505.5556 Combine like terms: 0 + 329505.5556 = 329505.5556 11.11111111x + x2 = 329505.5556 The x term is 11.11111111x. Take half its coefficient (5.555555555). Square it (30.86419752) and add it to both sides. Add '30.86419752' to each side of the equation. 11.11111111x + 30.86419752 + x2 = 329505.5556 + 30.86419752 Reorder the terms: 30.86419752 + 11.11111111x + x2 = 329505.5556 + 30.86419752 Combine like terms: 329505.5556 + 30.86419752 = 329536.41979752 30.86419752 + 11.11111111x + x2 = 329536.41979752 Factor a perfect square on the left side: (x + 5.555555555)(x + 5.555555555) = 329536.41979752 Calculate the square root of the right side: 574.052628073 Break this problem into two subproblems by setting (x + 5.555555555) equal to 574.052628073 and -574.052628073.Subproblem 1
x + 5.555555555 = 574.052628073 Simplifying x + 5.555555555 = 574.052628073 Reorder the terms: 5.555555555 + x = 574.052628073 Solving 5.555555555 + x = 574.052628073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.555555555' to each side of the equation. 5.555555555 + -5.555555555 + x = 574.052628073 + -5.555555555 Combine like terms: 5.555555555 + -5.555555555 = 0.000000000 0.000000000 + x = 574.052628073 + -5.555555555 x = 574.052628073 + -5.555555555 Combine like terms: 574.052628073 + -5.555555555 = 568.497072518 x = 568.497072518 Simplifying x = 568.497072518Subproblem 2
x + 5.555555555 = -574.052628073 Simplifying x + 5.555555555 = -574.052628073 Reorder the terms: 5.555555555 + x = -574.052628073 Solving 5.555555555 + x = -574.052628073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.555555555' to each side of the equation. 5.555555555 + -5.555555555 + x = -574.052628073 + -5.555555555 Combine like terms: 5.555555555 + -5.555555555 = 0.000000000 0.000000000 + x = -574.052628073 + -5.555555555 x = -574.052628073 + -5.555555555 Combine like terms: -574.052628073 + -5.555555555 = -579.608183628 x = -579.608183628 Simplifying x = -579.608183628Solution
The solution to the problem is based on the solutions from the subproblems. x = {568.497072518, -579.608183628}
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