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Simplifying 11x2 + 34x + -55 = 0 Reorder the terms: -55 + 34x + 11x2 = 0 Solving -55 + 34x + 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'. -5 + 3.090909091x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3.090909091x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 3.090909091x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3.090909091x + x2 = 0 + 5 3.090909091x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 3.090909091x + x2 = 5 The x term is 3.090909091x. Take half its coefficient (1.545454546). Square it (2.388429754) and add it to both sides. Add '2.388429754' to each side of the equation. 3.090909091x + 2.388429754 + x2 = 5 + 2.388429754 Reorder the terms: 2.388429754 + 3.090909091x + x2 = 5 + 2.388429754 Combine like terms: 5 + 2.388429754 = 7.388429754 2.388429754 + 3.090909091x + x2 = 7.388429754 Factor a perfect square on the left side: (x + 1.545454546)(x + 1.545454546) = 7.388429754 Calculate the square root of the right side: 2.718166616 Break this problem into two subproblems by setting (x + 1.545454546) equal to 2.718166616 and -2.718166616.Subproblem 1
x + 1.545454546 = 2.718166616 Simplifying x + 1.545454546 = 2.718166616 Reorder the terms: 1.545454546 + x = 2.718166616 Solving 1.545454546 + x = 2.718166616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.545454546' to each side of the equation. 1.545454546 + -1.545454546 + x = 2.718166616 + -1.545454546 Combine like terms: 1.545454546 + -1.545454546 = 0.000000000 0.000000000 + x = 2.718166616 + -1.545454546 x = 2.718166616 + -1.545454546 Combine like terms: 2.718166616 + -1.545454546 = 1.17271207 x = 1.17271207 Simplifying x = 1.17271207Subproblem 2
x + 1.545454546 = -2.718166616 Simplifying x + 1.545454546 = -2.718166616 Reorder the terms: 1.545454546 + x = -2.718166616 Solving 1.545454546 + x = -2.718166616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.545454546' to each side of the equation. 1.545454546 + -1.545454546 + x = -2.718166616 + -1.545454546 Combine like terms: 1.545454546 + -1.545454546 = 0.000000000 0.000000000 + x = -2.718166616 + -1.545454546 x = -2.718166616 + -1.545454546 Combine like terms: -2.718166616 + -1.545454546 = -4.263621162 x = -4.263621162 Simplifying x = -4.263621162Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.17271207, -4.263621162}
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