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Simplifying 9x2 + -61x + 4 = 0 Reorder the terms: 4 + -61x + 9x2 = 0 Solving 4 + -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'. 0.4444444444 + -6.777777778x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -6.777777778x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -6.777777778x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -6.777777778x + x2 = 0 + -0.4444444444 -6.777777778x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -6.777777778x + x2 = -0.4444444444 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 = -0.4444444444 + 11.48456790 Reorder the terms: 11.48456790 + -6.777777778x + x2 = -0.4444444444 + 11.48456790 Combine like terms: -0.4444444444 + 11.48456790 = 11.0401234556 11.48456790 + -6.777777778x + x2 = 11.0401234556 Factor a perfect square on the left side: (x + -3.388888889)(x + -3.388888889) = 11.0401234556 Calculate the square root of the right side: 3.322668123 Break this problem into two subproblems by setting (x + -3.388888889) equal to 3.322668123 and -3.322668123.Subproblem 1
x + -3.388888889 = 3.322668123 Simplifying x + -3.388888889 = 3.322668123 Reorder the terms: -3.388888889 + x = 3.322668123 Solving -3.388888889 + x = 3.322668123 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 = 3.322668123 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + x = 3.322668123 + 3.388888889 x = 3.322668123 + 3.388888889 Combine like terms: 3.322668123 + 3.388888889 = 6.711557012 x = 6.711557012 Simplifying x = 6.711557012Subproblem 2
x + -3.388888889 = -3.322668123 Simplifying x + -3.388888889 = -3.322668123 Reorder the terms: -3.388888889 + x = -3.322668123 Solving -3.388888889 + x = -3.322668123 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 = -3.322668123 + 3.388888889 Combine like terms: -3.388888889 + 3.388888889 = 0.000000000 0.000000000 + x = -3.322668123 + 3.388888889 x = -3.322668123 + 3.388888889 Combine like terms: -3.322668123 + 3.388888889 = 0.066220766 x = 0.066220766 Simplifying x = 0.066220766Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.711557012, 0.066220766}
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