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Simplifying 9x2 + 25x + -30 = 0 Reorder the terms: -30 + 25x + 9x2 = 0 Solving -30 + 25x + 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 + 2.777777778x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 2.777777778x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 2.777777778x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 2.777777778x + x2 = 0 + 3.333333333 2.777777778x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 2.777777778x + x2 = 3.333333333 The x term is 2.777777778x. Take half its coefficient (1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. 2.777777778x + 1.929012346 + x2 = 3.333333333 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778x + x2 = 3.333333333 + 1.929012346 Combine like terms: 3.333333333 + 1.929012346 = 5.262345679 1.929012346 + 2.777777778x + x2 = 5.262345679 Factor a perfect square on the left side: (x + 1.388888889)(x + 1.388888889) = 5.262345679 Calculate the square root of the right side: 2.293980314 Break this problem into two subproblems by setting (x + 1.388888889) equal to 2.293980314 and -2.293980314.Subproblem 1
x + 1.388888889 = 2.293980314 Simplifying x + 1.388888889 = 2.293980314 Reorder the terms: 1.388888889 + x = 2.293980314 Solving 1.388888889 + x = 2.293980314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.388888889' to each side of the equation. 1.388888889 + -1.388888889 + x = 2.293980314 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = 2.293980314 + -1.388888889 x = 2.293980314 + -1.388888889 Combine like terms: 2.293980314 + -1.388888889 = 0.905091425 x = 0.905091425 Simplifying x = 0.905091425Subproblem 2
x + 1.388888889 = -2.293980314 Simplifying x + 1.388888889 = -2.293980314 Reorder the terms: 1.388888889 + x = -2.293980314 Solving 1.388888889 + x = -2.293980314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.388888889' to each side of the equation. 1.388888889 + -1.388888889 + x = -2.293980314 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = -2.293980314 + -1.388888889 x = -2.293980314 + -1.388888889 Combine like terms: -2.293980314 + -1.388888889 = -3.682869203 x = -3.682869203 Simplifying x = -3.682869203Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.905091425, -3.682869203}
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