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Simplifying 2w2 + 6w + -560 = 0 Reorder the terms: -560 + 6w + 2w2 = 0 Solving -560 + 6w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-280 + 3w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-280 + 3w + w2)' equal to zero and attempt to solve: Simplifying -280 + 3w + w2 = 0 Solving -280 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '280' to each side of the equation. -280 + 3w + 280 + w2 = 0 + 280 Reorder the terms: -280 + 280 + 3w + w2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + 3w + w2 = 0 + 280 3w + w2 = 0 + 280 Combine like terms: 0 + 280 = 280 3w + w2 = 280 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 = 280 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 280 + 2.25 Combine like terms: 280 + 2.25 = 282.25 2.25 + 3w + w2 = 282.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (w + 1.5) equal to 16.800297616 and -16.800297616.Subproblem 1
w + 1.5 = 16.800297616 Simplifying w + 1.5 = 16.800297616 Reorder the terms: 1.5 + w = 16.800297616 Solving 1.5 + w = 16.800297616 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 = 16.800297616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 16.800297616 + -1.5 w = 16.800297616 + -1.5 Combine like terms: 16.800297616 + -1.5 = 15.300297616 w = 15.300297616 Simplifying w = 15.300297616Subproblem 2
w + 1.5 = -16.800297616 Simplifying w + 1.5 = -16.800297616 Reorder the terms: 1.5 + w = -16.800297616 Solving 1.5 + w = -16.800297616 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 = -16.800297616 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -16.800297616 + -1.5 w = -16.800297616 + -1.5 Combine like terms: -16.800297616 + -1.5 = -18.300297616 w = -18.300297616 Simplifying w = -18.300297616Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.300297616, -18.300297616}Solution
w = {15.300297616, -18.300297616}
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