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Simplifying 0 = 3w + 3w2 + -629 Reorder the terms: 0 = -629 + 3w + 3w2 Solving 0 = -629 + 3w + 3w2 Solving for variable 'w'. Combine like terms: 0 + 629 = 629 629 + -3w + -3w2 = -629 + 3w + 3w2 + 629 + -3w + -3w2 Reorder the terms: 629 + -3w + -3w2 = -629 + 629 + 3w + -3w + 3w2 + -3w2 Combine like terms: -629 + 629 = 0 629 + -3w + -3w2 = 0 + 3w + -3w + 3w2 + -3w2 629 + -3w + -3w2 = 3w + -3w + 3w2 + -3w2 Combine like terms: 3w + -3w = 0 629 + -3w + -3w2 = 0 + 3w2 + -3w2 629 + -3w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 629 + -3w + -3w2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -209.6666667 + w + w2 = 0 Move the constant term to the right: Add '209.6666667' to each side of the equation. -209.6666667 + w + 209.6666667 + w2 = 0 + 209.6666667 Reorder the terms: -209.6666667 + 209.6666667 + w + w2 = 0 + 209.6666667 Combine like terms: -209.6666667 + 209.6666667 = 0.0000000 0.0000000 + w + w2 = 0 + 209.6666667 w + w2 = 0 + 209.6666667 Combine like terms: 0 + 209.6666667 = 209.6666667 w + w2 = 209.6666667 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + w2 = 209.6666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + w2 = 209.6666667 + 0.25 Combine like terms: 209.6666667 + 0.25 = 209.9166667 1.25 + w2 = 209.9166667 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 209.9166667 Calculate the square root of the right side: 14.488501189 Break this problem into two subproblems by setting (w + 0.5) equal to 14.488501189 and -14.488501189.Subproblem 1
w + 0.5 = 14.488501189 Simplifying w + 0.5 = 14.488501189 Reorder the terms: 0.5 + w = 14.488501189 Solving 0.5 + w = 14.488501189 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 14.488501189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 14.488501189 + -0.5 w = 14.488501189 + -0.5 Combine like terms: 14.488501189 + -0.5 = 13.988501189 w = 13.988501189 Simplifying w = 13.988501189Subproblem 2
w + 0.5 = -14.488501189 Simplifying w + 0.5 = -14.488501189 Reorder the terms: 0.5 + w = -14.488501189 Solving 0.5 + w = -14.488501189 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -14.488501189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -14.488501189 + -0.5 w = -14.488501189 + -0.5 Combine like terms: -14.488501189 + -0.5 = -14.988501189 w = -14.988501189 Simplifying w = -14.988501189Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.988501189, -14.988501189}
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