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Simplifying w2 + 20w = 165 Reorder the terms: 20w + w2 = 165 Solving 20w + w2 = 165 Solving for variable 'w'. Reorder the terms: -165 + 20w + w2 = 165 + -165 Combine like terms: 165 + -165 = 0 -165 + 20w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '165' to each side of the equation. -165 + 20w + 165 + w2 = 0 + 165 Reorder the terms: -165 + 165 + 20w + w2 = 0 + 165 Combine like terms: -165 + 165 = 0 0 + 20w + w2 = 0 + 165 20w + w2 = 0 + 165 Combine like terms: 0 + 165 = 165 20w + w2 = 165 The w term is 20w. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20w + 100 + w2 = 165 + 100 Reorder the terms: 100 + 20w + w2 = 165 + 100 Combine like terms: 165 + 100 = 265 100 + 20w + w2 = 265 Factor a perfect square on the left side: (w + 10)(w + 10) = 265 Calculate the square root of the right side: 16.278820596 Break this problem into two subproblems by setting (w + 10) equal to 16.278820596 and -16.278820596.Subproblem 1
w + 10 = 16.278820596 Simplifying w + 10 = 16.278820596 Reorder the terms: 10 + w = 16.278820596 Solving 10 + w = 16.278820596 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = 16.278820596 + -10 Combine like terms: 10 + -10 = 0 0 + w = 16.278820596 + -10 w = 16.278820596 + -10 Combine like terms: 16.278820596 + -10 = 6.278820596 w = 6.278820596 Simplifying w = 6.278820596Subproblem 2
w + 10 = -16.278820596 Simplifying w + 10 = -16.278820596 Reorder the terms: 10 + w = -16.278820596 Solving 10 + w = -16.278820596 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = -16.278820596 + -10 Combine like terms: 10 + -10 = 0 0 + w = -16.278820596 + -10 w = -16.278820596 + -10 Combine like terms: -16.278820596 + -10 = -26.278820596 w = -26.278820596 Simplifying w = -26.278820596Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.278820596, -26.278820596}
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