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Simplifying 11x2 + -25x + -72 = 0 Reorder the terms: -72 + -25x + 11x2 = 0 Solving -72 + -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'. -6.545454545 + -2.272727273x + x2 = 0 Move the constant term to the right: Add '6.545454545' to each side of the equation. -6.545454545 + -2.272727273x + 6.545454545 + x2 = 0 + 6.545454545 Reorder the terms: -6.545454545 + 6.545454545 + -2.272727273x + x2 = 0 + 6.545454545 Combine like terms: -6.545454545 + 6.545454545 = 0.000000000 0.000000000 + -2.272727273x + x2 = 0 + 6.545454545 -2.272727273x + x2 = 0 + 6.545454545 Combine like terms: 0 + 6.545454545 = 6.545454545 -2.272727273x + x2 = 6.545454545 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 = 6.545454545 + 1.291322316 Reorder the terms: 1.291322316 + -2.272727273x + x2 = 6.545454545 + 1.291322316 Combine like terms: 6.545454545 + 1.291322316 = 7.836776861 1.291322316 + -2.272727273x + x2 = 7.836776861 Factor a perfect square on the left side: (x + -1.136363637)(x + -1.136363637) = 7.836776861 Calculate the square root of the right side: 2.79942438 Break this problem into two subproblems by setting (x + -1.136363637) equal to 2.79942438 and -2.79942438.Subproblem 1
x + -1.136363637 = 2.79942438 Simplifying x + -1.136363637 = 2.79942438 Reorder the terms: -1.136363637 + x = 2.79942438 Solving -1.136363637 + x = 2.79942438 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 = 2.79942438 + 1.136363637 Combine like terms: -1.136363637 + 1.136363637 = 0.000000000 0.000000000 + x = 2.79942438 + 1.136363637 x = 2.79942438 + 1.136363637 Combine like terms: 2.79942438 + 1.136363637 = 3.935788017 x = 3.935788017 Simplifying x = 3.935788017Subproblem 2
x + -1.136363637 = -2.79942438 Simplifying x + -1.136363637 = -2.79942438 Reorder the terms: -1.136363637 + x = -2.79942438 Solving -1.136363637 + x = -2.79942438 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 = -2.79942438 + 1.136363637 Combine like terms: -1.136363637 + 1.136363637 = 0.000000000 0.000000000 + x = -2.79942438 + 1.136363637 x = -2.79942438 + 1.136363637 Combine like terms: -2.79942438 + 1.136363637 = -1.663060743 x = -1.663060743 Simplifying x = -1.663060743Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.935788017, -1.663060743}
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