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Simplifying 9x2 + 43x + 30 = 0 Reorder the terms: 30 + 43x + 9x2 = 0 Solving 30 + 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'. 3.333333333 + 4.777777778x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 4.777777778x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 4.777777778x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 4.777777778x + x2 = 0 + -3.333333333 4.777777778x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 4.777777778x + x2 = -3.333333333 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 = -3.333333333 + 5.706790124 Reorder the terms: 5.706790124 + 4.777777778x + x2 = -3.333333333 + 5.706790124 Combine like terms: -3.333333333 + 5.706790124 = 2.373456791 5.706790124 + 4.777777778x + x2 = 2.373456791 Factor a perfect square on the left side: (x + 2.388888889)(x + 2.388888889) = 2.373456791 Calculate the square root of the right side: 1.540602736 Break this problem into two subproblems by setting (x + 2.388888889) equal to 1.540602736 and -1.540602736.Subproblem 1
x + 2.388888889 = 1.540602736 Simplifying x + 2.388888889 = 1.540602736 Reorder the terms: 2.388888889 + x = 1.540602736 Solving 2.388888889 + x = 1.540602736 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 = 1.540602736 + -2.388888889 Combine like terms: 2.388888889 + -2.388888889 = 0.000000000 0.000000000 + x = 1.540602736 + -2.388888889 x = 1.540602736 + -2.388888889 Combine like terms: 1.540602736 + -2.388888889 = -0.848286153 x = -0.848286153 Simplifying x = -0.848286153Subproblem 2
x + 2.388888889 = -1.540602736 Simplifying x + 2.388888889 = -1.540602736 Reorder the terms: 2.388888889 + x = -1.540602736 Solving 2.388888889 + x = -1.540602736 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 = -1.540602736 + -2.388888889 Combine like terms: 2.388888889 + -2.388888889 = 0.000000000 0.000000000 + x = -1.540602736 + -2.388888889 x = -1.540602736 + -2.388888889 Combine like terms: -1.540602736 + -2.388888889 = -3.929491625 x = -3.929491625 Simplifying x = -3.929491625Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.848286153, -3.929491625}
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