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Simplifying 11x2 + 5x + -44 = 0 Reorder the terms: -44 + 5x + 11x2 = 0 Solving -44 + 5x + 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'. -4 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.4545454545x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.4545454545x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.4545454545x + x2 = 0 + 4 0.4545454545x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.4545454545x + x2 = 4 The x term is 0.4545454545x. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545x + 0.05165289257 + x2 = 4 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = 4 + 0.05165289257 Combine like terms: 4 + 0.05165289257 = 4.05165289257 0.05165289257 + 0.4545454545x + x2 = 4.05165289257 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = 4.05165289257 Calculate the square root of the right side: 2.012871802 Break this problem into two subproblems by setting (x + 0.2272727273) equal to 2.012871802 and -2.012871802.Subproblem 1
x + 0.2272727273 = 2.012871802 Simplifying x + 0.2272727273 = 2.012871802 Reorder the terms: 0.2272727273 + x = 2.012871802 Solving 0.2272727273 + x = 2.012871802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = 2.012871802 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = 2.012871802 + -0.2272727273 x = 2.012871802 + -0.2272727273 Combine like terms: 2.012871802 + -0.2272727273 = 1.7855990747 x = 1.7855990747 Simplifying x = 1.7855990747Subproblem 2
x + 0.2272727273 = -2.012871802 Simplifying x + 0.2272727273 = -2.012871802 Reorder the terms: 0.2272727273 + x = -2.012871802 Solving 0.2272727273 + x = -2.012871802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = -2.012871802 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = -2.012871802 + -0.2272727273 x = -2.012871802 + -0.2272727273 Combine like terms: -2.012871802 + -0.2272727273 = -2.2401445293 x = -2.2401445293 Simplifying x = -2.2401445293Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7855990747, -2.2401445293}
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