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Simplifying 25x + 52 = 11x2 Reorder the terms: 52 + 25x = 11x2 Solving 52 + 25x = 11x2 Solving for variable 'x'. Combine like terms: 11x2 + -11x2 = 0 52 + 25x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -4.727272727 + -2.272727273x + x2 = 0 Move the constant term to the right: Add '4.727272727' to each side of the equation. -4.727272727 + -2.272727273x + 4.727272727 + x2 = 0 + 4.727272727 Reorder the terms: -4.727272727 + 4.727272727 + -2.272727273x + x2 = 0 + 4.727272727 Combine like terms: -4.727272727 + 4.727272727 = 0.000000000 0.000000000 + -2.272727273x + x2 = 0 + 4.727272727 -2.272727273x + x2 = 0 + 4.727272727 Combine like terms: 0 + 4.727272727 = 4.727272727 -2.272727273x + x2 = 4.727272727 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 = 4.727272727 + 1.291322316 Reorder the terms: 1.291322316 + -2.272727273x + x2 = 4.727272727 + 1.291322316 Combine like terms: 4.727272727 + 1.291322316 = 6.018595043 1.291322316 + -2.272727273x + x2 = 6.018595043 Factor a perfect square on the left side: (x + -1.136363637)(x + -1.136363637) = 6.018595043 Calculate the square root of the right side: 2.453282504 Break this problem into two subproblems by setting (x + -1.136363637) equal to 2.453282504 and -2.453282504.Subproblem 1
x + -1.136363637 = 2.453282504 Simplifying x + -1.136363637 = 2.453282504 Reorder the terms: -1.136363637 + x = 2.453282504 Solving -1.136363637 + x = 2.453282504 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 = 2.453282504 + 1.136363637 Combine like terms: -1.136363637 + 1.136363637 = 0.000000000 0.000000000 + x = 2.453282504 + 1.136363637 x = 2.453282504 + 1.136363637 Combine like terms: 2.453282504 + 1.136363637 = 3.589646141 x = 3.589646141 Simplifying x = 3.589646141Subproblem 2
x + -1.136363637 = -2.453282504 Simplifying x + -1.136363637 = -2.453282504 Reorder the terms: -1.136363637 + x = -2.453282504 Solving -1.136363637 + x = -2.453282504 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 = -2.453282504 + 1.136363637 Combine like terms: -1.136363637 + 1.136363637 = 0.000000000 0.000000000 + x = -2.453282504 + 1.136363637 x = -2.453282504 + 1.136363637 Combine like terms: -2.453282504 + 1.136363637 = -1.316918867 x = -1.316918867 Simplifying x = -1.316918867Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.589646141, -1.316918867}
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