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Simplifying 22x2 + -19x + -18 = 0 Reorder the terms: -18 + -19x + 22x2 = 0 Solving -18 + -19x + 22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -0.8181818182 + -0.8636363636x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + -0.8636363636x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + -0.8636363636x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + -0.8636363636x + x2 = 0 + 0.8181818182 -0.8636363636x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 -0.8636363636x + x2 = 0.8181818182 The x term is -0.8636363636x. Take half its coefficient (-0.4318181818). Square it (0.1864669421) and add it to both sides. Add '0.1864669421' to each side of the equation. -0.8636363636x + 0.1864669421 + x2 = 0.8181818182 + 0.1864669421 Reorder the terms: 0.1864669421 + -0.8636363636x + x2 = 0.8181818182 + 0.1864669421 Combine like terms: 0.8181818182 + 0.1864669421 = 1.0046487603 0.1864669421 + -0.8636363636x + x2 = 1.0046487603 Factor a perfect square on the left side: (x + -0.4318181818)(x + -0.4318181818) = 1.0046487603 Calculate the square root of the right side: 1.002321685 Break this problem into two subproblems by setting (x + -0.4318181818) equal to 1.002321685 and -1.002321685.Subproblem 1
x + -0.4318181818 = 1.002321685 Simplifying x + -0.4318181818 = 1.002321685 Reorder the terms: -0.4318181818 + x = 1.002321685 Solving -0.4318181818 + x = 1.002321685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4318181818' to each side of the equation. -0.4318181818 + 0.4318181818 + x = 1.002321685 + 0.4318181818 Combine like terms: -0.4318181818 + 0.4318181818 = 0.0000000000 0.0000000000 + x = 1.002321685 + 0.4318181818 x = 1.002321685 + 0.4318181818 Combine like terms: 1.002321685 + 0.4318181818 = 1.4341398668 x = 1.4341398668 Simplifying x = 1.4341398668Subproblem 2
x + -0.4318181818 = -1.002321685 Simplifying x + -0.4318181818 = -1.002321685 Reorder the terms: -0.4318181818 + x = -1.002321685 Solving -0.4318181818 + x = -1.002321685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4318181818' to each side of the equation. -0.4318181818 + 0.4318181818 + x = -1.002321685 + 0.4318181818 Combine like terms: -0.4318181818 + 0.4318181818 = 0.0000000000 0.0000000000 + x = -1.002321685 + 0.4318181818 x = -1.002321685 + 0.4318181818 Combine like terms: -1.002321685 + 0.4318181818 = -0.5705035032 x = -0.5705035032 Simplifying x = -0.5705035032Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4341398668, -0.5705035032}
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