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Simplifying 11x2 + 44x + 13 = 0 Reorder the terms: 13 + 44x + 11x2 = 0 Solving 13 + 44x + 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 + 4x + x2 = 0 Move the constant term to the right: Add '-1.181818182' to each side of the equation. 1.181818182 + 4x + -1.181818182 + x2 = 0 + -1.181818182 Reorder the terms: 1.181818182 + -1.181818182 + 4x + x2 = 0 + -1.181818182 Combine like terms: 1.181818182 + -1.181818182 = 0.000000000 0.000000000 + 4x + x2 = 0 + -1.181818182 4x + x2 = 0 + -1.181818182 Combine like terms: 0 + -1.181818182 = -1.181818182 4x + x2 = -1.181818182 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1.181818182 + 4 Reorder the terms: 4 + 4x + x2 = -1.181818182 + 4 Combine like terms: -1.181818182 + 4 = 2.818181818 4 + 4x + x2 = 2.818181818 Factor a perfect square on the left side: (x + 2)(x + 2) = 2.818181818 Calculate the square root of the right side: 1.678744119 Break this problem into two subproblems by setting (x + 2) equal to 1.678744119 and -1.678744119.Subproblem 1
x + 2 = 1.678744119 Simplifying x + 2 = 1.678744119 Reorder the terms: 2 + x = 1.678744119 Solving 2 + x = 1.678744119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.678744119 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.678744119 + -2 x = 1.678744119 + -2 Combine like terms: 1.678744119 + -2 = -0.321255881 x = -0.321255881 Simplifying x = -0.321255881Subproblem 2
x + 2 = -1.678744119 Simplifying x + 2 = -1.678744119 Reorder the terms: 2 + x = -1.678744119 Solving 2 + x = -1.678744119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.678744119 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.678744119 + -2 x = -1.678744119 + -2 Combine like terms: -1.678744119 + -2 = -3.678744119 x = -3.678744119 Simplifying x = -3.678744119Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.321255881, -3.678744119}
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