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Simplifying 6w2 + 17 = -9w + 5w2 Reorder the terms: 17 + 6w2 = -9w + 5w2 Solving 17 + 6w2 = -9w + 5w2 Solving for variable 'w'. Reorder the terms: 17 + 9w + 6w2 + -5w2 = -9w + 5w2 + 9w + -5w2 Combine like terms: 6w2 + -5w2 = 1w2 17 + 9w + 1w2 = -9w + 5w2 + 9w + -5w2 Reorder the terms: 17 + 9w + 1w2 = -9w + 9w + 5w2 + -5w2 Combine like terms: -9w + 9w = 0 17 + 9w + 1w2 = 0 + 5w2 + -5w2 17 + 9w + 1w2 = 5w2 + -5w2 Combine like terms: 5w2 + -5w2 = 0 17 + 9w + 1w2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 9w + -17 + w2 = 0 + -17 Reorder the terms: 17 + -17 + 9w + w2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 9w + w2 = 0 + -17 9w + w2 = 0 + -17 Combine like terms: 0 + -17 = -17 9w + w2 = -17 The w term is 9w. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9w + 20.25 + w2 = -17 + 20.25 Reorder the terms: 20.25 + 9w + w2 = -17 + 20.25 Combine like terms: -17 + 20.25 = 3.25 20.25 + 9w + w2 = 3.25 Factor a perfect square on the left side: (w + 4.5)(w + 4.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (w + 4.5) equal to 1.802775638 and -1.802775638.Subproblem 1
w + 4.5 = 1.802775638 Simplifying w + 4.5 = 1.802775638 Reorder the terms: 4.5 + w = 1.802775638 Solving 4.5 + w = 1.802775638 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = 1.802775638 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = 1.802775638 + -4.5 w = 1.802775638 + -4.5 Combine like terms: 1.802775638 + -4.5 = -2.697224362 w = -2.697224362 Simplifying w = -2.697224362Subproblem 2
w + 4.5 = -1.802775638 Simplifying w + 4.5 = -1.802775638 Reorder the terms: 4.5 + w = -1.802775638 Solving 4.5 + w = -1.802775638 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = -1.802775638 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = -1.802775638 + -4.5 w = -1.802775638 + -4.5 Combine like terms: -1.802775638 + -4.5 = -6.302775638 w = -6.302775638 Simplifying w = -6.302775638Solution
The solution to the problem is based on the solutions from the subproblems. w = {-2.697224362, -6.302775638}
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