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Simplifying 0.36x2 + -8x + -6000 = 0 Reorder the terms: -6000 + -8x + 0.36x2 = 0 Solving -6000 + -8x + 0.36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.36 the coefficient of the squared term: Divide each side by '0.36'. -16666.66667 + -22.22222222x + x2 = 0 Move the constant term to the right: Add '16666.66667' to each side of the equation. -16666.66667 + -22.22222222x + 16666.66667 + x2 = 0 + 16666.66667 Reorder the terms: -16666.66667 + 16666.66667 + -22.22222222x + x2 = 0 + 16666.66667 Combine like terms: -16666.66667 + 16666.66667 = 0.00000 0.00000 + -22.22222222x + x2 = 0 + 16666.66667 -22.22222222x + x2 = 0 + 16666.66667 Combine like terms: 0 + 16666.66667 = 16666.66667 -22.22222222x + x2 = 16666.66667 The x term is -22.22222222x. Take half its coefficient (-11.11111111). Square it (123.4567901) and add it to both sides. Add '123.4567901' to each side of the equation. -22.22222222x + 123.4567901 + x2 = 16666.66667 + 123.4567901 Reorder the terms: 123.4567901 + -22.22222222x + x2 = 16666.66667 + 123.4567901 Combine like terms: 16666.66667 + 123.4567901 = 16790.1234601 123.4567901 + -22.22222222x + x2 = 16790.1234601 Factor a perfect square on the left side: (x + -11.11111111)(x + -11.11111111) = 16790.1234601 Calculate the square root of the right side: 129.576708787 Break this problem into two subproblems by setting (x + -11.11111111) equal to 129.576708787 and -129.576708787.Subproblem 1
x + -11.11111111 = 129.576708787 Simplifying x + -11.11111111 = 129.576708787 Reorder the terms: -11.11111111 + x = 129.576708787 Solving -11.11111111 + x = 129.576708787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.11111111' to each side of the equation. -11.11111111 + 11.11111111 + x = 129.576708787 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + x = 129.576708787 + 11.11111111 x = 129.576708787 + 11.11111111 Combine like terms: 129.576708787 + 11.11111111 = 140.687819897 x = 140.687819897 Simplifying x = 140.687819897Subproblem 2
x + -11.11111111 = -129.576708787 Simplifying x + -11.11111111 = -129.576708787 Reorder the terms: -11.11111111 + x = -129.576708787 Solving -11.11111111 + x = -129.576708787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.11111111' to each side of the equation. -11.11111111 + 11.11111111 + x = -129.576708787 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + x = -129.576708787 + 11.11111111 x = -129.576708787 + 11.11111111 Combine like terms: -129.576708787 + 11.11111111 = -118.465597677 x = -118.465597677 Simplifying x = -118.465597677Solution
The solution to the problem is based on the solutions from the subproblems. x = {140.687819897, -118.465597677}
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