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Simplifying w2 + -86w + 450 = 0 Reorder the terms: 450 + -86w + w2 = 0 Solving 450 + -86w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-450' to each side of the equation. 450 + -86w + -450 + w2 = 0 + -450 Reorder the terms: 450 + -450 + -86w + w2 = 0 + -450 Combine like terms: 450 + -450 = 0 0 + -86w + w2 = 0 + -450 -86w + w2 = 0 + -450 Combine like terms: 0 + -450 = -450 -86w + w2 = -450 The w term is -86w. Take half its coefficient (-43). Square it (1849) and add it to both sides. Add '1849' to each side of the equation. -86w + 1849 + w2 = -450 + 1849 Reorder the terms: 1849 + -86w + w2 = -450 + 1849 Combine like terms: -450 + 1849 = 1399 1849 + -86w + w2 = 1399 Factor a perfect square on the left side: (w + -43)(w + -43) = 1399 Calculate the square root of the right side: 37.403208419 Break this problem into two subproblems by setting (w + -43) equal to 37.403208419 and -37.403208419.Subproblem 1
w + -43 = 37.403208419 Simplifying w + -43 = 37.403208419 Reorder the terms: -43 + w = 37.403208419 Solving -43 + w = 37.403208419 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + w = 37.403208419 + 43 Combine like terms: -43 + 43 = 0 0 + w = 37.403208419 + 43 w = 37.403208419 + 43 Combine like terms: 37.403208419 + 43 = 80.403208419 w = 80.403208419 Simplifying w = 80.403208419Subproblem 2
w + -43 = -37.403208419 Simplifying w + -43 = -37.403208419 Reorder the terms: -43 + w = -37.403208419 Solving -43 + w = -37.403208419 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + w = -37.403208419 + 43 Combine like terms: -43 + 43 = 0 0 + w = -37.403208419 + 43 w = -37.403208419 + 43 Combine like terms: -37.403208419 + 43 = 5.596791581 w = 5.596791581 Simplifying w = 5.596791581Solution
The solution to the problem is based on the solutions from the subproblems. w = {80.403208419, 5.596791581}
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