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Simplifying 11x2 + -5x + -46 = 0 Reorder the terms: -46 + -5x + 11x2 = 0 Solving -46 + -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'. -4.181818182 + -0.4545454545x + x2 = 0 Move the constant term to the right: Add '4.181818182' to each side of the equation. -4.181818182 + -0.4545454545x + 4.181818182 + x2 = 0 + 4.181818182 Reorder the terms: -4.181818182 + 4.181818182 + -0.4545454545x + x2 = 0 + 4.181818182 Combine like terms: -4.181818182 + 4.181818182 = 0.000000000 0.000000000 + -0.4545454545x + x2 = 0 + 4.181818182 -0.4545454545x + x2 = 0 + 4.181818182 Combine like terms: 0 + 4.181818182 = 4.181818182 -0.4545454545x + x2 = 4.181818182 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 = 4.181818182 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545x + x2 = 4.181818182 + 0.05165289257 Combine like terms: 4.181818182 + 0.05165289257 = 4.23347107457 0.05165289257 + -0.4545454545x + x2 = 4.23347107457 Factor a perfect square on the left side: (x + -0.2272727273)(x + -0.2272727273) = 4.23347107457 Calculate the square root of the right side: 2.057540054 Break this problem into two subproblems by setting (x + -0.2272727273) equal to 2.057540054 and -2.057540054.Subproblem 1
x + -0.2272727273 = 2.057540054 Simplifying x + -0.2272727273 = 2.057540054 Reorder the terms: -0.2272727273 + x = 2.057540054 Solving -0.2272727273 + x = 2.057540054 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 = 2.057540054 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = 2.057540054 + 0.2272727273 x = 2.057540054 + 0.2272727273 Combine like terms: 2.057540054 + 0.2272727273 = 2.2848127813 x = 2.2848127813 Simplifying x = 2.2848127813Subproblem 2
x + -0.2272727273 = -2.057540054 Simplifying x + -0.2272727273 = -2.057540054 Reorder the terms: -0.2272727273 + x = -2.057540054 Solving -0.2272727273 + x = -2.057540054 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 = -2.057540054 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = -2.057540054 + 0.2272727273 x = -2.057540054 + 0.2272727273 Combine like terms: -2.057540054 + 0.2272727273 = -1.8302673267 x = -1.8302673267 Simplifying x = -1.8302673267Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2848127813, -1.8302673267}
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