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Simplifying 55w2 + 22w + -3 = 0 Reorder the terms: -3 + 22w + 55w2 = 0 Solving -3 + 22w + 55w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 55 the coefficient of the squared term: Divide each side by '55'. -0.05454545455 + 0.4w + w2 = 0 Move the constant term to the right: Add '0.05454545455' to each side of the equation. -0.05454545455 + 0.4w + 0.05454545455 + w2 = 0 + 0.05454545455 Reorder the terms: -0.05454545455 + 0.05454545455 + 0.4w + w2 = 0 + 0.05454545455 Combine like terms: -0.05454545455 + 0.05454545455 = 0.00000000000 0.00000000000 + 0.4w + w2 = 0 + 0.05454545455 0.4w + w2 = 0 + 0.05454545455 Combine like terms: 0 + 0.05454545455 = 0.05454545455 0.4w + w2 = 0.05454545455 The w term is 0.4w. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4w + 0.04 + w2 = 0.05454545455 + 0.04 Reorder the terms: 0.04 + 0.4w + w2 = 0.05454545455 + 0.04 Combine like terms: 0.05454545455 + 0.04 = 0.09454545455 0.04 + 0.4w + w2 = 0.09454545455 Factor a perfect square on the left side: (w + 0.2)(w + 0.2) = 0.09454545455 Calculate the square root of the right side: 0.307482446 Break this problem into two subproblems by setting (w + 0.2) equal to 0.307482446 and -0.307482446.Subproblem 1
w + 0.2 = 0.307482446 Simplifying w + 0.2 = 0.307482446 Reorder the terms: 0.2 + w = 0.307482446 Solving 0.2 + w = 0.307482446 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + w = 0.307482446 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + w = 0.307482446 + -0.2 w = 0.307482446 + -0.2 Combine like terms: 0.307482446 + -0.2 = 0.107482446 w = 0.107482446 Simplifying w = 0.107482446Subproblem 2
w + 0.2 = -0.307482446 Simplifying w + 0.2 = -0.307482446 Reorder the terms: 0.2 + w = -0.307482446 Solving 0.2 + w = -0.307482446 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + w = -0.307482446 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + w = -0.307482446 + -0.2 w = -0.307482446 + -0.2 Combine like terms: -0.307482446 + -0.2 = -0.507482446 w = -0.507482446 Simplifying w = -0.507482446Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.107482446, -0.507482446}
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