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Simplifying 33 = w(w + 5) Reorder the terms: 33 = w(5 + w) 33 = (5 * w + w * w) 33 = (5w + w2) Solving 33 = 5w + w2 Solving for variable 'w'. Reorder the terms: 33 + -5w + -1w2 = 5w + -5w + w2 + -1w2 Combine like terms: 5w + -5w = 0 33 + -5w + -1w2 = 0 + w2 + -1w2 33 + -5w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 33 + -5w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -33 + 5w + w2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 5w + 33 + w2 = 0 + 33 Reorder the terms: -33 + 33 + 5w + w2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 5w + w2 = 0 + 33 5w + w2 = 0 + 33 Combine like terms: 0 + 33 = 33 5w + w2 = 33 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = 33 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 33 + 6.25 Combine like terms: 33 + 6.25 = 39.25 6.25 + 5w + w2 = 39.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (w + 2.5) equal to 6.264982043 and -6.264982043.Subproblem 1
w + 2.5 = 6.264982043 Simplifying w + 2.5 = 6.264982043 Reorder the terms: 2.5 + w = 6.264982043 Solving 2.5 + w = 6.264982043 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 6.264982043 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 6.264982043 + -2.5 w = 6.264982043 + -2.5 Combine like terms: 6.264982043 + -2.5 = 3.764982043 w = 3.764982043 Simplifying w = 3.764982043Subproblem 2
w + 2.5 = -6.264982043 Simplifying w + 2.5 = -6.264982043 Reorder the terms: 2.5 + w = -6.264982043 Solving 2.5 + w = -6.264982043 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -6.264982043 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -6.264982043 + -2.5 w = -6.264982043 + -2.5 Combine like terms: -6.264982043 + -2.5 = -8.764982043 w = -8.764982043 Simplifying w = -8.764982043Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.764982043, -8.764982043}
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