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Simplifying (9x2 + -4x + -56) + (9x2 + 9x) = 0 Reorder the terms: (-56 + -4x + 9x2) + (9x2 + 9x) = 0 Remove parenthesis around (-56 + -4x + 9x2) -56 + -4x + 9x2 + (9x2 + 9x) = 0 Reorder the terms: -56 + -4x + 9x2 + (9x + 9x2) = 0 Remove parenthesis around (9x + 9x2) -56 + -4x + 9x2 + 9x + 9x2 = 0 Reorder the terms: -56 + -4x + 9x + 9x2 + 9x2 = 0 Combine like terms: -4x + 9x = 5x -56 + 5x + 9x2 + 9x2 = 0 Combine like terms: 9x2 + 9x2 = 18x2 -56 + 5x + 18x2 = 0 Solving -56 + 5x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -3.111111111 + 0.2777777778x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + 0.2777777778x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + 0.2777777778x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + 0.2777777778x + x2 = 0 + 3.111111111 0.2777777778x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 0.2777777778x + x2 = 3.111111111 The x term is 0.2777777778x. Take half its coefficient (0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. 0.2777777778x + 0.01929012346 + x2 = 3.111111111 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778x + x2 = 3.111111111 + 0.01929012346 Combine like terms: 3.111111111 + 0.01929012346 = 3.13040123446 0.01929012346 + 0.2777777778x + x2 = 3.13040123446 Factor a perfect square on the left side: (x + 0.1388888889)(x + 0.1388888889) = 3.13040123446 Calculate the square root of the right side: 1.769293993 Break this problem into two subproblems by setting (x + 0.1388888889) equal to 1.769293993 and -1.769293993.Subproblem 1
x + 0.1388888889 = 1.769293993 Simplifying x + 0.1388888889 = 1.769293993 Reorder the terms: 0.1388888889 + x = 1.769293993 Solving 0.1388888889 + x = 1.769293993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + x = 1.769293993 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = 1.769293993 + -0.1388888889 x = 1.769293993 + -0.1388888889 Combine like terms: 1.769293993 + -0.1388888889 = 1.6304051041 x = 1.6304051041 Simplifying x = 1.6304051041Subproblem 2
x + 0.1388888889 = -1.769293993 Simplifying x + 0.1388888889 = -1.769293993 Reorder the terms: 0.1388888889 + x = -1.769293993 Solving 0.1388888889 + x = -1.769293993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.1388888889 + x = -1.769293993 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + x = -1.769293993 + -0.1388888889 x = -1.769293993 + -0.1388888889 Combine like terms: -1.769293993 + -0.1388888889 = -1.9081828819 x = -1.9081828819 Simplifying x = -1.9081828819Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6304051041, -1.9081828819}
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