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Simplifying w(w + 30) = 3600 Reorder the terms: w(30 + w) = 3600 (30 * w + w * w) = 3600 (30w + w2) = 3600 Solving 30w + w2 = 3600 Solving for variable 'w'. Reorder the terms: -3600 + 30w + w2 = 3600 + -3600 Combine like terms: 3600 + -3600 = 0 -3600 + 30w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 30w + 3600 + w2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 30w + w2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 30w + w2 = 0 + 3600 30w + w2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 30w + w2 = 3600 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 = 3600 + 225 Reorder the terms: 225 + 30w + w2 = 3600 + 225 Combine like terms: 3600 + 225 = 3825 225 + 30w + w2 = 3825 Factor a perfect square on the left side: (w + 15)(w + 15) = 3825 Calculate the square root of the right side: 61.846584384 Break this problem into two subproblems by setting (w + 15) equal to 61.846584384 and -61.846584384.Subproblem 1
w + 15 = 61.846584384 Simplifying w + 15 = 61.846584384 Reorder the terms: 15 + w = 61.846584384 Solving 15 + w = 61.846584384 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 = 61.846584384 + -15 Combine like terms: 15 + -15 = 0 0 + w = 61.846584384 + -15 w = 61.846584384 + -15 Combine like terms: 61.846584384 + -15 = 46.846584384 w = 46.846584384 Simplifying w = 46.846584384Subproblem 2
w + 15 = -61.846584384 Simplifying w + 15 = -61.846584384 Reorder the terms: 15 + w = -61.846584384 Solving 15 + w = -61.846584384 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 = -61.846584384 + -15 Combine like terms: 15 + -15 = 0 0 + w = -61.846584384 + -15 w = -61.846584384 + -15 Combine like terms: -61.846584384 + -15 = -76.846584384 w = -76.846584384 Simplifying w = -76.846584384Solution
The solution to the problem is based on the solutions from the subproblems. w = {46.846584384, -76.846584384}
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