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Simplifying 44w2 + w + -21 = 0 Reorder the terms: -21 + w + 44w2 = 0 Solving -21 + w + 44w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.4772727273 + 0.02272727273w + w2 = 0 Move the constant term to the right: Add '0.4772727273' to each side of the equation. -0.4772727273 + 0.02272727273w + 0.4772727273 + w2 = 0 + 0.4772727273 Reorder the terms: -0.4772727273 + 0.4772727273 + 0.02272727273w + w2 = 0 + 0.4772727273 Combine like terms: -0.4772727273 + 0.4772727273 = 0.0000000000 0.0000000000 + 0.02272727273w + w2 = 0 + 0.4772727273 0.02272727273w + w2 = 0 + 0.4772727273 Combine like terms: 0 + 0.4772727273 = 0.4772727273 0.02272727273w + w2 = 0.4772727273 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.02272727273w + 0.25 + w2 = 0.4772727273 + 0.25 Reorder the terms: 0.25 + 0.02272727273w + w2 = 0.4772727273 + 0.25 Combine like terms: 0.4772727273 + 0.25 = 0.7272727273 0.25 + 0.02272727273w + w2 = 0.7272727273 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 0.7272727273 Calculate the square root of the right side: 0.852802865 Break this problem into two subproblems by setting (w + 0.5) equal to 0.852802865 and -0.852802865.Subproblem 1
w + 0.5 = 0.852802865 Simplifying w + 0.5 = 0.852802865 Reorder the terms: 0.5 + w = 0.852802865 Solving 0.5 + w = 0.852802865 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 0.852802865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 0.852802865 + -0.5 w = 0.852802865 + -0.5 Combine like terms: 0.852802865 + -0.5 = 0.352802865 w = 0.352802865 Simplifying w = 0.352802865Subproblem 2
w + 0.5 = -0.852802865 Simplifying w + 0.5 = -0.852802865 Reorder the terms: 0.5 + w = -0.852802865 Solving 0.5 + w = -0.852802865 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -0.852802865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -0.852802865 + -0.5 w = -0.852802865 + -0.5 Combine like terms: -0.852802865 + -0.5 = -1.352802865 w = -1.352802865 Simplifying w = -1.352802865Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.352802865, -1.352802865}
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