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Simplifying 11x2 + 5x = 9 Reorder the terms: 5x + 11x2 = 9 Solving 5x + 11x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 5x + 11x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 5x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.8181818182 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + 0.4545454545x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + 0.4545454545x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + 0.4545454545x + x2 = 0 + 0.8181818182 0.4545454545x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 0.4545454545x + x2 = 0.8181818182 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 = 0.8181818182 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = 0.8181818182 + 0.05165289257 Combine like terms: 0.8181818182 + 0.05165289257 = 0.86983471077 0.05165289257 + 0.4545454545x + x2 = 0.86983471077 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = 0.86983471077 Calculate the square root of the right side: 0.932649297 Break this problem into two subproblems by setting (x + 0.2272727273) equal to 0.932649297 and -0.932649297.Subproblem 1
x + 0.2272727273 = 0.932649297 Simplifying x + 0.2272727273 = 0.932649297 Reorder the terms: 0.2272727273 + x = 0.932649297 Solving 0.2272727273 + x = 0.932649297 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 = 0.932649297 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = 0.932649297 + -0.2272727273 x = 0.932649297 + -0.2272727273 Combine like terms: 0.932649297 + -0.2272727273 = 0.7053765697 x = 0.7053765697 Simplifying x = 0.7053765697Subproblem 2
x + 0.2272727273 = -0.932649297 Simplifying x + 0.2272727273 = -0.932649297 Reorder the terms: 0.2272727273 + x = -0.932649297 Solving 0.2272727273 + x = -0.932649297 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 = -0.932649297 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = -0.932649297 + -0.2272727273 x = -0.932649297 + -0.2272727273 Combine like terms: -0.932649297 + -0.2272727273 = -1.1599220243 x = -1.1599220243 Simplifying x = -1.1599220243Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7053765697, -1.1599220243}
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