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Simplifying 9x2 + -41x + 44 = 0 Reorder the terms: 44 + -41x + 9x2 = 0 Solving 44 + -41x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4.888888889 + -4.555555556x + x2 = 0 Move the constant term to the right: Add '-4.888888889' to each side of the equation. 4.888888889 + -4.555555556x + -4.888888889 + x2 = 0 + -4.888888889 Reorder the terms: 4.888888889 + -4.888888889 + -4.555555556x + x2 = 0 + -4.888888889 Combine like terms: 4.888888889 + -4.888888889 = 0.000000000 0.000000000 + -4.555555556x + x2 = 0 + -4.888888889 -4.555555556x + x2 = 0 + -4.888888889 Combine like terms: 0 + -4.888888889 = -4.888888889 -4.555555556x + x2 = -4.888888889 The x term is -4.555555556x. Take half its coefficient (-2.277777778). Square it (5.188271606) and add it to both sides. Add '5.188271606' to each side of the equation. -4.555555556x + 5.188271606 + x2 = -4.888888889 + 5.188271606 Reorder the terms: 5.188271606 + -4.555555556x + x2 = -4.888888889 + 5.188271606 Combine like terms: -4.888888889 + 5.188271606 = 0.299382717 5.188271606 + -4.555555556x + x2 = 0.299382717 Factor a perfect square on the left side: (x + -2.277777778)(x + -2.277777778) = 0.299382717 Calculate the square root of the right side: 0.547158768 Break this problem into two subproblems by setting (x + -2.277777778) equal to 0.547158768 and -0.547158768.Subproblem 1
x + -2.277777778 = 0.547158768 Simplifying x + -2.277777778 = 0.547158768 Reorder the terms: -2.277777778 + x = 0.547158768 Solving -2.277777778 + x = 0.547158768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = 0.547158768 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = 0.547158768 + 2.277777778 x = 0.547158768 + 2.277777778 Combine like terms: 0.547158768 + 2.277777778 = 2.824936546 x = 2.824936546 Simplifying x = 2.824936546Subproblem 2
x + -2.277777778 = -0.547158768 Simplifying x + -2.277777778 = -0.547158768 Reorder the terms: -2.277777778 + x = -0.547158768 Solving -2.277777778 + x = -0.547158768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = -0.547158768 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = -0.547158768 + 2.277777778 x = -0.547158768 + 2.277777778 Combine like terms: -0.547158768 + 2.277777778 = 1.73061901 x = 1.73061901 Simplifying x = 1.73061901Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.824936546, 1.73061901}
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