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Simplifying 11x2 + -34x + 13 = 0 Reorder the terms: 13 + -34x + 11x2 = 0 Solving 13 + -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'. 1.181818182 + -3.090909091x + x2 = 0 Move the constant term to the right: Add '-1.181818182' to each side of the equation. 1.181818182 + -3.090909091x + -1.181818182 + x2 = 0 + -1.181818182 Reorder the terms: 1.181818182 + -1.181818182 + -3.090909091x + x2 = 0 + -1.181818182 Combine like terms: 1.181818182 + -1.181818182 = 0.000000000 0.000000000 + -3.090909091x + x2 = 0 + -1.181818182 -3.090909091x + x2 = 0 + -1.181818182 Combine like terms: 0 + -1.181818182 = -1.181818182 -3.090909091x + x2 = -1.181818182 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 = -1.181818182 + 2.388429754 Reorder the terms: 2.388429754 + -3.090909091x + x2 = -1.181818182 + 2.388429754 Combine like terms: -1.181818182 + 2.388429754 = 1.206611572 2.388429754 + -3.090909091x + x2 = 1.206611572 Factor a perfect square on the left side: (x + -1.545454546)(x + -1.545454546) = 1.206611572 Calculate the square root of the right side: 1.098458726 Break this problem into two subproblems by setting (x + -1.545454546) equal to 1.098458726 and -1.098458726.Subproblem 1
x + -1.545454546 = 1.098458726 Simplifying x + -1.545454546 = 1.098458726 Reorder the terms: -1.545454546 + x = 1.098458726 Solving -1.545454546 + x = 1.098458726 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 = 1.098458726 + 1.545454546 Combine like terms: -1.545454546 + 1.545454546 = 0.000000000 0.000000000 + x = 1.098458726 + 1.545454546 x = 1.098458726 + 1.545454546 Combine like terms: 1.098458726 + 1.545454546 = 2.643913272 x = 2.643913272 Simplifying x = 2.643913272Subproblem 2
x + -1.545454546 = -1.098458726 Simplifying x + -1.545454546 = -1.098458726 Reorder the terms: -1.545454546 + x = -1.098458726 Solving -1.545454546 + x = -1.098458726 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 = -1.098458726 + 1.545454546 Combine like terms: -1.545454546 + 1.545454546 = 0.000000000 0.000000000 + x = -1.098458726 + 1.545454546 x = -1.098458726 + 1.545454546 Combine like terms: -1.098458726 + 1.545454546 = 0.44699582 x = 0.44699582 Simplifying x = 0.44699582Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.643913272, 0.44699582}
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