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Simplifying 22W2 + -8W = 9 Reorder the terms: -8W + 22W2 = 9 Solving -8W + 22W2 = 9 Solving for variable 'W'. Reorder the terms: -9 + -8W + 22W2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -8W + 22W2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -0.4090909091 + -0.3636363636W + W2 = 0 Move the constant term to the right: Add '0.4090909091' to each side of the equation. -0.4090909091 + -0.3636363636W + 0.4090909091 + W2 = 0 + 0.4090909091 Reorder the terms: -0.4090909091 + 0.4090909091 + -0.3636363636W + W2 = 0 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + -0.3636363636W + W2 = 0 + 0.4090909091 -0.3636363636W + W2 = 0 + 0.4090909091 Combine like terms: 0 + 0.4090909091 = 0.4090909091 -0.3636363636W + W2 = 0.4090909091 The W term is -0.3636363636W. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636W + 0.03305785123 + W2 = 0.4090909091 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636W + W2 = 0.4090909091 + 0.03305785123 Combine like terms: 0.4090909091 + 0.03305785123 = 0.44214876033 0.03305785123 + -0.3636363636W + W2 = 0.44214876033 Factor a perfect square on the left side: (W + -0.1818181818)(W + -0.1818181818) = 0.44214876033 Calculate the square root of the right side: 0.664942674 Break this problem into two subproblems by setting (W + -0.1818181818) equal to 0.664942674 and -0.664942674.Subproblem 1
W + -0.1818181818 = 0.664942674 Simplifying W + -0.1818181818 = 0.664942674 Reorder the terms: -0.1818181818 + W = 0.664942674 Solving -0.1818181818 + W = 0.664942674 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + W = 0.664942674 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + W = 0.664942674 + 0.1818181818 W = 0.664942674 + 0.1818181818 Combine like terms: 0.664942674 + 0.1818181818 = 0.8467608558 W = 0.8467608558 Simplifying W = 0.8467608558Subproblem 2
W + -0.1818181818 = -0.664942674 Simplifying W + -0.1818181818 = -0.664942674 Reorder the terms: -0.1818181818 + W = -0.664942674 Solving -0.1818181818 + W = -0.664942674 Solving for variable 'W'. Move all terms containing W to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + W = -0.664942674 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + W = -0.664942674 + 0.1818181818 W = -0.664942674 + 0.1818181818 Combine like terms: -0.664942674 + 0.1818181818 = -0.4831244922 W = -0.4831244922 Simplifying W = -0.4831244922Solution
The solution to the problem is based on the solutions from the subproblems. W = {0.8467608558, -0.4831244922}
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