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Simplifying w = w2 + 2w + -35 Reorder the terms: w = -35 + 2w + w2 Solving w = -35 + 2w + w2 Solving for variable 'w'. Reorder the terms: 35 + w + -2w + -1w2 = -35 + 2w + w2 + 35 + -2w + -1w2 Combine like terms: w + -2w = -1w 35 + -1w + -1w2 = -35 + 2w + w2 + 35 + -2w + -1w2 Reorder the terms: 35 + -1w + -1w2 = -35 + 35 + 2w + -2w + w2 + -1w2 Combine like terms: -35 + 35 = 0 35 + -1w + -1w2 = 0 + 2w + -2w + w2 + -1w2 35 + -1w + -1w2 = 2w + -2w + w2 + -1w2 Combine like terms: 2w + -2w = 0 35 + -1w + -1w2 = 0 + w2 + -1w2 35 + -1w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 35 + -1w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + w + w2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + w + 35 + w2 = 0 + 35 Reorder the terms: -35 + 35 + w + w2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + w + w2 = 0 + 35 w + w2 = 0 + 35 Combine like terms: 0 + 35 = 35 w + w2 = 35 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. + 0.25 + w2 = 35 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + w2 = 35 + 0.25 Combine like terms: 35 + 0.25 = 35.25 1.25 + w2 = 35.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (w + 0.5) equal to 5.937171044 and -5.937171044.Subproblem 1
w + 0.5 = 5.937171044 Simplifying w + 0.5 = 5.937171044 Reorder the terms: 0.5 + w = 5.937171044 Solving 0.5 + w = 5.937171044 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 = 5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 5.937171044 + -0.5 w = 5.937171044 + -0.5 Combine like terms: 5.937171044 + -0.5 = 5.437171044 w = 5.437171044 Simplifying w = 5.437171044Subproblem 2
w + 0.5 = -5.937171044 Simplifying w + 0.5 = -5.937171044 Reorder the terms: 0.5 + w = -5.937171044 Solving 0.5 + w = -5.937171044 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 = -5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -5.937171044 + -0.5 w = -5.937171044 + -0.5 Combine like terms: -5.937171044 + -0.5 = -6.437171044 w = -6.437171044 Simplifying w = -6.437171044Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.437171044, -6.437171044}
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