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Simplifying 11x2 + -25x + -2 = 0 Reorder the terms: -2 + -25x + 11x2 = 0 Solving -2 + -25x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + -2.272727273x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -2.272727273x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -2.272727273x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -2.272727273x + x2 = 0 + 0.1818181818 -2.272727273x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -2.272727273x + x2 = 0.1818181818 The x term is -2.272727273x. Take half its coefficient (-1.136363637). Square it (1.291322316) and add it to both sides. Add '1.291322316' to each side of the equation. -2.272727273x + 1.291322316 + x2 = 0.1818181818 + 1.291322316 Reorder the terms: 1.291322316 + -2.272727273x + x2 = 0.1818181818 + 1.291322316 Combine like terms: 0.1818181818 + 1.291322316 = 1.4731404978 1.291322316 + -2.272727273x + x2 = 1.4731404978 Factor a perfect square on the left side: (x + -1.136363637)(x + -1.136363637) = 1.4731404978 Calculate the square root of the right side: 1.213729994 Break this problem into two subproblems by setting (x + -1.136363637) equal to 1.213729994 and -1.213729994.Subproblem 1
x + -1.136363637 = 1.213729994 Simplifying x + -1.136363637 = 1.213729994 Reorder the terms: -1.136363637 + x = 1.213729994 Solving -1.136363637 + x = 1.213729994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.136363637' to each side of the equation. -1.136363637 + 1.136363637 + x = 1.213729994 + 1.136363637 Combine like terms: -1.136363637 + 1.136363637 = 0.000000000 0.000000000 + x = 1.213729994 + 1.136363637 x = 1.213729994 + 1.136363637 Combine like terms: 1.213729994 + 1.136363637 = 2.350093631 x = 2.350093631 Simplifying x = 2.350093631Subproblem 2
x + -1.136363637 = -1.213729994 Simplifying x + -1.136363637 = -1.213729994 Reorder the terms: -1.136363637 + x = -1.213729994 Solving -1.136363637 + x = -1.213729994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.136363637' to each side of the equation. -1.136363637 + 1.136363637 + x = -1.213729994 + 1.136363637 Combine like terms: -1.136363637 + 1.136363637 = 0.000000000 0.000000000 + x = -1.213729994 + 1.136363637 x = -1.213729994 + 1.136363637 Combine like terms: -1.213729994 + 1.136363637 = -0.077366357 x = -0.077366357 Simplifying x = -0.077366357Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.350093631, -0.077366357}
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