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Simplifying -22x2 + -36x + -2 = 0 Reorder the terms: -2 + -36x + -22x2 = 0 Solving -2 + -36x + -22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + 18x + 11x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1 + 18x + 11x2)' equal to zero and attempt to solve: Simplifying 1 + 18x + 11x2 = 0 Solving 1 + 18x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.09090909091 + 1.636363636x + x2 = 0 Move the constant term to the right: Add '-0.09090909091' to each side of the equation. 0.09090909091 + 1.636363636x + -0.09090909091 + x2 = 0 + -0.09090909091 Reorder the terms: 0.09090909091 + -0.09090909091 + 1.636363636x + x2 = 0 + -0.09090909091 Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000 0.00000000000 + 1.636363636x + x2 = 0 + -0.09090909091 1.636363636x + x2 = 0 + -0.09090909091 Combine like terms: 0 + -0.09090909091 = -0.09090909091 1.636363636x + x2 = -0.09090909091 The x term is 1.636363636x. Take half its coefficient (0.818181818). Square it (0.6694214873) and add it to both sides. Add '0.6694214873' to each side of the equation. 1.636363636x + 0.6694214873 + x2 = -0.09090909091 + 0.6694214873 Reorder the terms: 0.6694214873 + 1.636363636x + x2 = -0.09090909091 + 0.6694214873 Combine like terms: -0.09090909091 + 0.6694214873 = 0.57851239639 0.6694214873 + 1.636363636x + x2 = 0.57851239639 Factor a perfect square on the left side: (x + 0.818181818)(x + 0.818181818) = 0.57851239639 Calculate the square root of the right side: 0.760600024 Break this problem into two subproblems by setting (x + 0.818181818) equal to 0.760600024 and -0.760600024.Subproblem 1
x + 0.818181818 = 0.760600024 Simplifying x + 0.818181818 = 0.760600024 Reorder the terms: 0.818181818 + x = 0.760600024 Solving 0.818181818 + x = 0.760600024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.818181818' to each side of the equation. 0.818181818 + -0.818181818 + x = 0.760600024 + -0.818181818 Combine like terms: 0.818181818 + -0.818181818 = 0.000000000 0.000000000 + x = 0.760600024 + -0.818181818 x = 0.760600024 + -0.818181818 Combine like terms: 0.760600024 + -0.818181818 = -0.057581794 x = -0.057581794 Simplifying x = -0.057581794Subproblem 2
x + 0.818181818 = -0.760600024 Simplifying x + 0.818181818 = -0.760600024 Reorder the terms: 0.818181818 + x = -0.760600024 Solving 0.818181818 + x = -0.760600024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.818181818' to each side of the equation. 0.818181818 + -0.818181818 + x = -0.760600024 + -0.818181818 Combine like terms: 0.818181818 + -0.818181818 = 0.000000000 0.000000000 + x = -0.760600024 + -0.818181818 x = -0.760600024 + -0.818181818 Combine like terms: -0.760600024 + -0.818181818 = -1.578781842 x = -1.578781842 Simplifying x = -1.578781842Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.057581794, -1.578781842}Solution
x = {-0.057581794, -1.578781842}
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