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Simplifying 480 = w(w + 30) Reorder the terms: 480 = w(30 + w) 480 = (30 * w + w * w) 480 = (30w + w2) Solving 480 = 30w + w2 Solving for variable 'w'. Reorder the terms: 480 + -30w + -1w2 = 30w + -30w + w2 + -1w2 Combine like terms: 30w + -30w = 0 480 + -30w + -1w2 = 0 + w2 + -1w2 480 + -30w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 480 + -30w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -480 + 30w + w2 = 0 Move the constant term to the right: Add '480' to each side of the equation. -480 + 30w + 480 + w2 = 0 + 480 Reorder the terms: -480 + 480 + 30w + w2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 30w + w2 = 0 + 480 30w + w2 = 0 + 480 Combine like terms: 0 + 480 = 480 30w + w2 = 480 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 = 480 + 225 Reorder the terms: 225 + 30w + w2 = 480 + 225 Combine like terms: 480 + 225 = 705 225 + 30w + w2 = 705 Factor a perfect square on the left side: (w + 15)(w + 15) = 705 Calculate the square root of the right side: 26.551836095 Break this problem into two subproblems by setting (w + 15) equal to 26.551836095 and -26.551836095.Subproblem 1
w + 15 = 26.551836095 Simplifying w + 15 = 26.551836095 Reorder the terms: 15 + w = 26.551836095 Solving 15 + w = 26.551836095 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 = 26.551836095 + -15 Combine like terms: 15 + -15 = 0 0 + w = 26.551836095 + -15 w = 26.551836095 + -15 Combine like terms: 26.551836095 + -15 = 11.551836095 w = 11.551836095 Simplifying w = 11.551836095Subproblem 2
w + 15 = -26.551836095 Simplifying w + 15 = -26.551836095 Reorder the terms: 15 + w = -26.551836095 Solving 15 + w = -26.551836095 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 = -26.551836095 + -15 Combine like terms: 15 + -15 = 0 0 + w = -26.551836095 + -15 w = -26.551836095 + -15 Combine like terms: -26.551836095 + -15 = -41.551836095 w = -41.551836095 Simplifying w = -41.551836095Solution
The solution to the problem is based on the solutions from the subproblems. w = {11.551836095, -41.551836095}
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