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Simplifying 22x2 + 8x + -61 = 0 Reorder the terms: -61 + 8x + 22x2 = 0 Solving -61 + 8x + 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'. -2.772727273 + 0.3636363636x + x2 = 0 Move the constant term to the right: Add '2.772727273' to each side of the equation. -2.772727273 + 0.3636363636x + 2.772727273 + x2 = 0 + 2.772727273 Reorder the terms: -2.772727273 + 2.772727273 + 0.3636363636x + x2 = 0 + 2.772727273 Combine like terms: -2.772727273 + 2.772727273 = 0.000000000 0.000000000 + 0.3636363636x + x2 = 0 + 2.772727273 0.3636363636x + x2 = 0 + 2.772727273 Combine like terms: 0 + 2.772727273 = 2.772727273 0.3636363636x + x2 = 2.772727273 The x term is 0.3636363636x. Take half its coefficient (0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. 0.3636363636x + 0.03305785123 + x2 = 2.772727273 + 0.03305785123 Reorder the terms: 0.03305785123 + 0.3636363636x + x2 = 2.772727273 + 0.03305785123 Combine like terms: 2.772727273 + 0.03305785123 = 2.80578512423 0.03305785123 + 0.3636363636x + x2 = 2.80578512423 Factor a perfect square on the left side: (x + 0.1818181818)(x + 0.1818181818) = 2.80578512423 Calculate the square root of the right side: 1.675047798 Break this problem into two subproblems by setting (x + 0.1818181818) equal to 1.675047798 and -1.675047798.Subproblem 1
x + 0.1818181818 = 1.675047798 Simplifying x + 0.1818181818 = 1.675047798 Reorder the terms: 0.1818181818 + x = 1.675047798 Solving 0.1818181818 + x = 1.675047798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = 1.675047798 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = 1.675047798 + -0.1818181818 x = 1.675047798 + -0.1818181818 Combine like terms: 1.675047798 + -0.1818181818 = 1.4932296162 x = 1.4932296162 Simplifying x = 1.4932296162Subproblem 2
x + 0.1818181818 = -1.675047798 Simplifying x + 0.1818181818 = -1.675047798 Reorder the terms: 0.1818181818 + x = -1.675047798 Solving 0.1818181818 + x = -1.675047798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = -1.675047798 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = -1.675047798 + -0.1818181818 x = -1.675047798 + -0.1818181818 Combine like terms: -1.675047798 + -0.1818181818 = -1.8568659798 x = -1.8568659798 Simplifying x = -1.8568659798Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4932296162, -1.8568659798}
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