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Simplifying 5.39x + 12.97x2 + -6.44 + -8.47x2 + -8.91 = 0 Reorder the terms: -6.44 + -8.91 + 5.39x + 12.97x2 + -8.47x2 = 0 Combine like terms: -6.44 + -8.91 = -15.35 -15.35 + 5.39x + 12.97x2 + -8.47x2 = 0 Combine like terms: 12.97x2 + -8.47x2 = 4.5x2 -15.35 + 5.39x + 4.5x2 = 0 Solving -15.35 + 5.39x + 4.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.5 the coefficient of the squared term: Divide each side by '4.5'. -3.411111111 + 1.197777778x + x2 = 0 Move the constant term to the right: Add '3.411111111' to each side of the equation. -3.411111111 + 1.197777778x + 3.411111111 + x2 = 0 + 3.411111111 Reorder the terms: -3.411111111 + 3.411111111 + 1.197777778x + x2 = 0 + 3.411111111 Combine like terms: -3.411111111 + 3.411111111 = 0.000000000 0.000000000 + 1.197777778x + x2 = 0 + 3.411111111 1.197777778x + x2 = 0 + 3.411111111 Combine like terms: 0 + 3.411111111 = 3.411111111 1.197777778x + x2 = 3.411111111 The x term is 1.197777778x. Take half its coefficient (0.598888889). Square it (0.3586679014) and add it to both sides. Add '0.3586679014' to each side of the equation. 1.197777778x + 0.3586679014 + x2 = 3.411111111 + 0.3586679014 Reorder the terms: 0.3586679014 + 1.197777778x + x2 = 3.411111111 + 0.3586679014 Combine like terms: 3.411111111 + 0.3586679014 = 3.7697790124 0.3586679014 + 1.197777778x + x2 = 3.7697790124 Factor a perfect square on the left side: (x + 0.598888889)(x + 0.598888889) = 3.7697790124 Calculate the square root of the right side: 1.941591876 Break this problem into two subproblems by setting (x + 0.598888889) equal to 1.941591876 and -1.941591876.Subproblem 1
x + 0.598888889 = 1.941591876 Simplifying x + 0.598888889 = 1.941591876 Reorder the terms: 0.598888889 + x = 1.941591876 Solving 0.598888889 + x = 1.941591876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.598888889' to each side of the equation. 0.598888889 + -0.598888889 + x = 1.941591876 + -0.598888889 Combine like terms: 0.598888889 + -0.598888889 = 0.000000000 0.000000000 + x = 1.941591876 + -0.598888889 x = 1.941591876 + -0.598888889 Combine like terms: 1.941591876 + -0.598888889 = 1.342702987 x = 1.342702987 Simplifying x = 1.342702987Subproblem 2
x + 0.598888889 = -1.941591876 Simplifying x + 0.598888889 = -1.941591876 Reorder the terms: 0.598888889 + x = -1.941591876 Solving 0.598888889 + x = -1.941591876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.598888889' to each side of the equation. 0.598888889 + -0.598888889 + x = -1.941591876 + -0.598888889 Combine like terms: 0.598888889 + -0.598888889 = 0.000000000 0.000000000 + x = -1.941591876 + -0.598888889 x = -1.941591876 + -0.598888889 Combine like terms: -1.941591876 + -0.598888889 = -2.540480765 x = -2.540480765 Simplifying x = -2.540480765Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.342702987, -2.540480765}
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