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Simplifying w(w + 180) = 40 Reorder the terms: w(180 + w) = 40 (180 * w + w * w) = 40 (180w + w2) = 40 Solving 180w + w2 = 40 Solving for variable 'w'. Reorder the terms: -40 + 180w + w2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 180w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 180w + 40 + w2 = 0 + 40 Reorder the terms: -40 + 40 + 180w + w2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 180w + w2 = 0 + 40 180w + w2 = 0 + 40 Combine like terms: 0 + 40 = 40 180w + w2 = 40 The w term is 180w. Take half its coefficient (90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. 180w + 8100 + w2 = 40 + 8100 Reorder the terms: 8100 + 180w + w2 = 40 + 8100 Combine like terms: 40 + 8100 = 8140 8100 + 180w + w2 = 8140 Factor a perfect square on the left side: (w + 90)(w + 90) = 8140 Calculate the square root of the right side: 90.221948549 Break this problem into two subproblems by setting (w + 90) equal to 90.221948549 and -90.221948549.Subproblem 1
w + 90 = 90.221948549 Simplifying w + 90 = 90.221948549 Reorder the terms: 90 + w = 90.221948549 Solving 90 + w = 90.221948549 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + w = 90.221948549 + -90 Combine like terms: 90 + -90 = 0 0 + w = 90.221948549 + -90 w = 90.221948549 + -90 Combine like terms: 90.221948549 + -90 = 0.221948549 w = 0.221948549 Simplifying w = 0.221948549Subproblem 2
w + 90 = -90.221948549 Simplifying w + 90 = -90.221948549 Reorder the terms: 90 + w = -90.221948549 Solving 90 + w = -90.221948549 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-90' to each side of the equation. 90 + -90 + w = -90.221948549 + -90 Combine like terms: 90 + -90 = 0 0 + w = -90.221948549 + -90 w = -90.221948549 + -90 Combine like terms: -90.221948549 + -90 = -180.221948549 w = -180.221948549 Simplifying w = -180.221948549Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.221948549, -180.221948549}
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