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Simplifying (9x2) + -61x + 2 = 0 Reorder the terms: 2 + -61x + (9x2) = 0 Solving 2 + -61x + (9x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + -6.777777778x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -6.777777778x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -6.777777778x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -6.777777778x + x2 = 0 + -0.2222222222 -6.777777778x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -6.777777778x + x2 = -0.2222222222 The x term is -6.777777778x. Take half its coefficient (-3.388888889). Square it (11.48456790) and add it to both sides. Add '11.48456790' to each side of the equation. -6.777777778x + 11.48456790 + x2 = -0.2222222222 + 11.48456790 Reorder the terms: 11.48456790 + -6.777777778x + x2 = -0.2222222222 + 11.48456790 Combine like terms: -0.2222222222 + 11.48456790 = 11.2623456778 11.48456790 + -6.777777778x + x2 = 11.2623456778 Factor a perfect square on the left side: ((x) + -3.388888889)((x) + -3.388888889) = 11.2623456778 Calculate the square root of the right side: 3.355941847 Break this problem into two subproblems by setting ((x) + -3.388888889) equal to 3.355941847 and -3.355941847.Subproblem 1
(x) + -3.388888889 = 3.355941847 Simplifying (x) + -3.388888889 = 3.355941847 x + -3.388888889 = 3.355941847 Reorder the terms: -3.388888889 + x = 3.355941847 Solving -3.388888889 + x = 3.355941847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.388888889' to each side of the equation. -3.388888889 + 3.388888889 + x = 3.355941847 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + x = 3.355941847 + 3.388888889 x = 3.355941847 + 3.388888889 Combine like terms: 3.355941847 + 3.388888889 = 6.744830736 x = 6.744830736 Simplifying x = 6.744830736Subproblem 2
(x) + -3.388888889 = -3.355941847 Simplifying (x) + -3.388888889 = -3.355941847 x + -3.388888889 = -3.355941847 Reorder the terms: -3.388888889 + x = -3.355941847 Solving -3.388888889 + x = -3.355941847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.388888889' to each side of the equation. -3.388888889 + 3.388888889 + x = -3.355941847 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + x = -3.355941847 + 3.388888889 x = -3.355941847 + 3.388888889 Combine like terms: -3.355941847 + 3.388888889 = 0.032947042 x = 0.032947042 Simplifying x = 0.032947042Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.744830736, 0.032947042}
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