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Simplifying 208 + 2 = w2 + 3w Combine like terms: 208 + 2 = 210 210 = w2 + 3w Reorder the terms: 210 = 3w + w2 Solving 210 = 3w + w2 Solving for variable 'w'. Reorder the terms: 210 + -3w + -1w2 = 3w + -3w + w2 + -1w2 Combine like terms: 3w + -3w = 0 210 + -3w + -1w2 = 0 + w2 + -1w2 210 + -3w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 210 + -3w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -210 + 3w + w2 = 0 Move the constant term to the right: Add '210' to each side of the equation. -210 + 3w + 210 + w2 = 0 + 210 Reorder the terms: -210 + 210 + 3w + w2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + 3w + w2 = 0 + 210 3w + w2 = 0 + 210 Combine like terms: 0 + 210 = 210 3w + w2 = 210 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 210 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 210 + 2.25 Combine like terms: 210 + 2.25 = 212.25 2.25 + 3w + w2 = 212.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 212.25 Calculate the square root of the right side: 14.568802284 Break this problem into two subproblems by setting (w + 1.5) equal to 14.568802284 and -14.568802284.Subproblem 1
w + 1.5 = 14.568802284 Simplifying w + 1.5 = 14.568802284 Reorder the terms: 1.5 + w = 14.568802284 Solving 1.5 + w = 14.568802284 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 14.568802284 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 14.568802284 + -1.5 w = 14.568802284 + -1.5 Combine like terms: 14.568802284 + -1.5 = 13.068802284 w = 13.068802284 Simplifying w = 13.068802284Subproblem 2
w + 1.5 = -14.568802284 Simplifying w + 1.5 = -14.568802284 Reorder the terms: 1.5 + w = -14.568802284 Solving 1.5 + w = -14.568802284 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -14.568802284 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -14.568802284 + -1.5 w = -14.568802284 + -1.5 Combine like terms: -14.568802284 + -1.5 = -16.068802284 w = -16.068802284 Simplifying w = -16.068802284Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.068802284, -16.068802284}
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