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Simplifying 22x2 + 80x + -840 = 0 Reorder the terms: -840 + 80x + 22x2 = 0 Solving -840 + 80x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-420 + 40x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-420 + 40x + 11x2)' equal to zero and attempt to solve: Simplifying -420 + 40x + 11x2 = 0 Solving -420 + 40x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -38.18181818 + 3.636363636x + x2 = 0 Move the constant term to the right: Add '38.18181818' to each side of the equation. -38.18181818 + 3.636363636x + 38.18181818 + x2 = 0 + 38.18181818 Reorder the terms: -38.18181818 + 38.18181818 + 3.636363636x + x2 = 0 + 38.18181818 Combine like terms: -38.18181818 + 38.18181818 = 0.00000000 0.00000000 + 3.636363636x + x2 = 0 + 38.18181818 3.636363636x + x2 = 0 + 38.18181818 Combine like terms: 0 + 38.18181818 = 38.18181818 3.636363636x + x2 = 38.18181818 The x term is 3.636363636x. Take half its coefficient (1.818181818). Square it (3.305785123) and add it to both sides. Add '3.305785123' to each side of the equation. 3.636363636x + 3.305785123 + x2 = 38.18181818 + 3.305785123 Reorder the terms: 3.305785123 + 3.636363636x + x2 = 38.18181818 + 3.305785123 Combine like terms: 38.18181818 + 3.305785123 = 41.487603303 3.305785123 + 3.636363636x + x2 = 41.487603303 Factor a perfect square on the left side: (x + 1.818181818)(x + 1.818181818) = 41.487603303 Calculate the square root of the right side: 6.441087121 Break this problem into two subproblems by setting (x + 1.818181818) equal to 6.441087121 and -6.441087121.Subproblem 1
x + 1.818181818 = 6.441087121 Simplifying x + 1.818181818 = 6.441087121 Reorder the terms: 1.818181818 + x = 6.441087121 Solving 1.818181818 + x = 6.441087121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.818181818' to each side of the equation. 1.818181818 + -1.818181818 + x = 6.441087121 + -1.818181818 Combine like terms: 1.818181818 + -1.818181818 = 0.000000000 0.000000000 + x = 6.441087121 + -1.818181818 x = 6.441087121 + -1.818181818 Combine like terms: 6.441087121 + -1.818181818 = 4.622905303 x = 4.622905303 Simplifying x = 4.622905303Subproblem 2
x + 1.818181818 = -6.441087121 Simplifying x + 1.818181818 = -6.441087121 Reorder the terms: 1.818181818 + x = -6.441087121 Solving 1.818181818 + x = -6.441087121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.818181818' to each side of the equation. 1.818181818 + -1.818181818 + x = -6.441087121 + -1.818181818 Combine like terms: 1.818181818 + -1.818181818 = 0.000000000 0.000000000 + x = -6.441087121 + -1.818181818 x = -6.441087121 + -1.818181818 Combine like terms: -6.441087121 + -1.818181818 = -8.259268939 x = -8.259268939 Simplifying x = -8.259268939Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.622905303, -8.259268939}Solution
x = {4.622905303, -8.259268939}
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