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Simplifying 9x2 + 43x + 49 = 0 Reorder the terms: 49 + 43x + 9x2 = 0 Solving 49 + 43x + 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'. 5.444444444 + 4.777777778x + x2 = 0 Move the constant term to the right: Add '-5.444444444' to each side of the equation. 5.444444444 + 4.777777778x + -5.444444444 + x2 = 0 + -5.444444444 Reorder the terms: 5.444444444 + -5.444444444 + 4.777777778x + x2 = 0 + -5.444444444 Combine like terms: 5.444444444 + -5.444444444 = 0.000000000 0.000000000 + 4.777777778x + x2 = 0 + -5.444444444 4.777777778x + x2 = 0 + -5.444444444 Combine like terms: 0 + -5.444444444 = -5.444444444 4.777777778x + x2 = -5.444444444 The x term is 4.777777778x. Take half its coefficient (2.388888889). Square it (5.706790124) and add it to both sides. Add '5.706790124' to each side of the equation. 4.777777778x + 5.706790124 + x2 = -5.444444444 + 5.706790124 Reorder the terms: 5.706790124 + 4.777777778x + x2 = -5.444444444 + 5.706790124 Combine like terms: -5.444444444 + 5.706790124 = 0.26234568 5.706790124 + 4.777777778x + x2 = 0.26234568 Factor a perfect square on the left side: (x + 2.388888889)(x + 2.388888889) = 0.26234568 Calculate the square root of the right side: 0.512196915 Break this problem into two subproblems by setting (x + 2.388888889) equal to 0.512196915 and -0.512196915.Subproblem 1
x + 2.388888889 = 0.512196915 Simplifying x + 2.388888889 = 0.512196915 Reorder the terms: 2.388888889 + x = 0.512196915 Solving 2.388888889 + x = 0.512196915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.388888889' to each side of the equation. 2.388888889 + -2.388888889 + x = 0.512196915 + -2.388888889 Combine like terms: 2.388888889 + -2.388888889 = 0.000000000 0.000000000 + x = 0.512196915 + -2.388888889 x = 0.512196915 + -2.388888889 Combine like terms: 0.512196915 + -2.388888889 = -1.876691974 x = -1.876691974 Simplifying x = -1.876691974Subproblem 2
x + 2.388888889 = -0.512196915 Simplifying x + 2.388888889 = -0.512196915 Reorder the terms: 2.388888889 + x = -0.512196915 Solving 2.388888889 + x = -0.512196915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.388888889' to each side of the equation. 2.388888889 + -2.388888889 + x = -0.512196915 + -2.388888889 Combine like terms: 2.388888889 + -2.388888889 = 0.000000000 0.000000000 + x = -0.512196915 + -2.388888889 x = -0.512196915 + -2.388888889 Combine like terms: -0.512196915 + -2.388888889 = -2.901085804 x = -2.901085804 Simplifying x = -2.901085804Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.876691974, -2.901085804}
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