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Simplifying 0.81x2 + -9x + -7000 = 0 Reorder the terms: -7000 + -9x + 0.81x2 = 0 Solving -7000 + -9x + 0.81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.81 the coefficient of the squared term: Divide each side by '0.81'. -8641.975309 + -11.11111111x + x2 = 0 Move the constant term to the right: Add '8641.975309' to each side of the equation. -8641.975309 + -11.11111111x + 8641.975309 + x2 = 0 + 8641.975309 Reorder the terms: -8641.975309 + 8641.975309 + -11.11111111x + x2 = 0 + 8641.975309 Combine like terms: -8641.975309 + 8641.975309 = 0.000000 0.000000 + -11.11111111x + x2 = 0 + 8641.975309 -11.11111111x + x2 = 0 + 8641.975309 Combine like terms: 0 + 8641.975309 = 8641.975309 -11.11111111x + x2 = 8641.975309 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 = 8641.975309 + 30.86419752 Reorder the terms: 30.86419752 + -11.11111111x + x2 = 8641.975309 + 30.86419752 Combine like terms: 8641.975309 + 30.86419752 = 8672.83950652 30.86419752 + -11.11111111x + x2 = 8672.83950652 Factor a perfect square on the left side: (x + -5.555555555)(x + -5.555555555) = 8672.83950652 Calculate the square root of the right side: 93.128081192 Break this problem into two subproblems by setting (x + -5.555555555) equal to 93.128081192 and -93.128081192.Subproblem 1
x + -5.555555555 = 93.128081192 Simplifying x + -5.555555555 = 93.128081192 Reorder the terms: -5.555555555 + x = 93.128081192 Solving -5.555555555 + x = 93.128081192 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 = 93.128081192 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = 93.128081192 + 5.555555555 x = 93.128081192 + 5.555555555 Combine like terms: 93.128081192 + 5.555555555 = 98.683636747 x = 98.683636747 Simplifying x = 98.683636747Subproblem 2
x + -5.555555555 = -93.128081192 Simplifying x + -5.555555555 = -93.128081192 Reorder the terms: -5.555555555 + x = -93.128081192 Solving -5.555555555 + x = -93.128081192 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 = -93.128081192 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = -93.128081192 + 5.555555555 x = -93.128081192 + 5.555555555 Combine like terms: -93.128081192 + 5.555555555 = -87.572525637 x = -87.572525637 Simplifying x = -87.572525637Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.683636747, -87.572525637}
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