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Simplifying w2 + 30w = 880 Reorder the terms: 30w + w2 = 880 Solving 30w + w2 = 880 Solving for variable 'w'. Reorder the terms: -880 + 30w + w2 = 880 + -880 Combine like terms: 880 + -880 = 0 -880 + 30w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '880' to each side of the equation. -880 + 30w + 880 + w2 = 0 + 880 Reorder the terms: -880 + 880 + 30w + w2 = 0 + 880 Combine like terms: -880 + 880 = 0 0 + 30w + w2 = 0 + 880 30w + w2 = 0 + 880 Combine like terms: 0 + 880 = 880 30w + w2 = 880 The w term is 30w. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30w + 225 + w2 = 880 + 225 Reorder the terms: 225 + 30w + w2 = 880 + 225 Combine like terms: 880 + 225 = 1105 225 + 30w + w2 = 1105 Factor a perfect square on the left side: (w + 15)(w + 15) = 1105 Calculate the square root of the right side: 33.241540277 Break this problem into two subproblems by setting (w + 15) equal to 33.241540277 and -33.241540277.Subproblem 1
w + 15 = 33.241540277 Simplifying w + 15 = 33.241540277 Reorder the terms: 15 + w = 33.241540277 Solving 15 + w = 33.241540277 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = 33.241540277 + -15 Combine like terms: 15 + -15 = 0 0 + w = 33.241540277 + -15 w = 33.241540277 + -15 Combine like terms: 33.241540277 + -15 = 18.241540277 w = 18.241540277 Simplifying w = 18.241540277Subproblem 2
w + 15 = -33.241540277 Simplifying w + 15 = -33.241540277 Reorder the terms: 15 + w = -33.241540277 Solving 15 + w = -33.241540277 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + w = -33.241540277 + -15 Combine like terms: 15 + -15 = 0 0 + w = -33.241540277 + -15 w = -33.241540277 + -15 Combine like terms: -33.241540277 + -15 = -48.241540277 w = -48.241540277 Simplifying w = -48.241540277Solution
The solution to the problem is based on the solutions from the subproblems. w = {18.241540277, -48.241540277}
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