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Simplifying 33w2 + 52w + 5 = 0 Reorder the terms: 5 + 52w + 33w2 = 0 Solving 5 + 52w + 33w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. 0.1515151515 + 1.575757576w + w2 = 0 Move the constant term to the right: Add '-0.1515151515' to each side of the equation. 0.1515151515 + 1.575757576w + -0.1515151515 + w2 = 0 + -0.1515151515 Reorder the terms: 0.1515151515 + -0.1515151515 + 1.575757576w + w2 = 0 + -0.1515151515 Combine like terms: 0.1515151515 + -0.1515151515 = 0.0000000000 0.0000000000 + 1.575757576w + w2 = 0 + -0.1515151515 1.575757576w + w2 = 0 + -0.1515151515 Combine like terms: 0 + -0.1515151515 = -0.1515151515 1.575757576w + w2 = -0.1515151515 The w term is 1.575757576w. Take half its coefficient (0.787878788). Square it (0.6207529846) and add it to both sides. Add '0.6207529846' to each side of the equation. 1.575757576w + 0.6207529846 + w2 = -0.1515151515 + 0.6207529846 Reorder the terms: 0.6207529846 + 1.575757576w + w2 = -0.1515151515 + 0.6207529846 Combine like terms: -0.1515151515 + 0.6207529846 = 0.4692378331 0.6207529846 + 1.575757576w + w2 = 0.4692378331 Factor a perfect square on the left side: (w + 0.787878788)(w + 0.787878788) = 0.4692378331 Calculate the square root of the right side: 0.685009367 Break this problem into two subproblems by setting (w + 0.787878788) equal to 0.685009367 and -0.685009367.Subproblem 1
w + 0.787878788 = 0.685009367 Simplifying w + 0.787878788 = 0.685009367 Reorder the terms: 0.787878788 + w = 0.685009367 Solving 0.787878788 + w = 0.685009367 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.787878788' to each side of the equation. 0.787878788 + -0.787878788 + w = 0.685009367 + -0.787878788 Combine like terms: 0.787878788 + -0.787878788 = 0.000000000 0.000000000 + w = 0.685009367 + -0.787878788 w = 0.685009367 + -0.787878788 Combine like terms: 0.685009367 + -0.787878788 = -0.102869421 w = -0.102869421 Simplifying w = -0.102869421Subproblem 2
w + 0.787878788 = -0.685009367 Simplifying w + 0.787878788 = -0.685009367 Reorder the terms: 0.787878788 + w = -0.685009367 Solving 0.787878788 + w = -0.685009367 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.787878788' to each side of the equation. 0.787878788 + -0.787878788 + w = -0.685009367 + -0.787878788 Combine like terms: 0.787878788 + -0.787878788 = 0.000000000 0.000000000 + w = -0.685009367 + -0.787878788 w = -0.685009367 + -0.787878788 Combine like terms: -0.685009367 + -0.787878788 = -1.472888155 w = -1.472888155 Simplifying w = -1.472888155Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.102869421, -1.472888155}
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