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Simplifying 4x2 + -14x + 5 + -11x + -13x2 = 0 Reorder the terms: 5 + -14x + -11x + 4x2 + -13x2 = 0 Combine like terms: -14x + -11x = -25x 5 + -25x + 4x2 + -13x2 = 0 Combine like terms: 4x2 + -13x2 = -9x2 5 + -25x + -9x2 = 0 Solving 5 + -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'. -0.5555555556 + 2.777777778x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 2.777777778x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 2.777777778x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 2.777777778x + x2 = 0 + 0.5555555556 2.777777778x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 2.777777778x + x2 = 0.5555555556 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 = 0.5555555556 + 1.929012346 Reorder the terms: 1.929012346 + 2.777777778x + x2 = 0.5555555556 + 1.929012346 Combine like terms: 0.5555555556 + 1.929012346 = 2.4845679016 1.929012346 + 2.777777778x + x2 = 2.4845679016 Factor a perfect square on the left side: (x + 1.388888889)(x + 1.388888889) = 2.4845679016 Calculate the square root of the right side: 1.576251218 Break this problem into two subproblems by setting (x + 1.388888889) equal to 1.576251218 and -1.576251218.Subproblem 1
x + 1.388888889 = 1.576251218 Simplifying x + 1.388888889 = 1.576251218 Reorder the terms: 1.388888889 + x = 1.576251218 Solving 1.388888889 + x = 1.576251218 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 = 1.576251218 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = 1.576251218 + -1.388888889 x = 1.576251218 + -1.388888889 Combine like terms: 1.576251218 + -1.388888889 = 0.187362329 x = 0.187362329 Simplifying x = 0.187362329Subproblem 2
x + 1.388888889 = -1.576251218 Simplifying x + 1.388888889 = -1.576251218 Reorder the terms: 1.388888889 + x = -1.576251218 Solving 1.388888889 + x = -1.576251218 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 = -1.576251218 + -1.388888889 Combine like terms: 1.388888889 + -1.388888889 = 0.000000000 0.000000000 + x = -1.576251218 + -1.388888889 x = -1.576251218 + -1.388888889 Combine like terms: -1.576251218 + -1.388888889 = -2.965140107 x = -2.965140107 Simplifying x = -2.965140107Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.187362329, -2.965140107}
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