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Simplifying w2 + 15w + 35 = 0 Reorder the terms: 35 + 15w + w2 = 0 Solving 35 + 15w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 15w + -35 + w2 = 0 + -35 Reorder the terms: 35 + -35 + 15w + w2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 15w + w2 = 0 + -35 15w + w2 = 0 + -35 Combine like terms: 0 + -35 = -35 15w + w2 = -35 The w term is 15w. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15w + 56.25 + w2 = -35 + 56.25 Reorder the terms: 56.25 + 15w + w2 = -35 + 56.25 Combine like terms: -35 + 56.25 = 21.25 56.25 + 15w + w2 = 21.25 Factor a perfect square on the left side: (w + 7.5)(w + 7.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (w + 7.5) equal to 4.609772229 and -4.609772229.Subproblem 1
w + 7.5 = 4.609772229 Simplifying w + 7.5 = 4.609772229 Reorder the terms: 7.5 + w = 4.609772229 Solving 7.5 + w = 4.609772229 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = 4.609772229 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 4.609772229 + -7.5 w = 4.609772229 + -7.5 Combine like terms: 4.609772229 + -7.5 = -2.890227771 w = -2.890227771 Simplifying w = -2.890227771Subproblem 2
w + 7.5 = -4.609772229 Simplifying w + 7.5 = -4.609772229 Reorder the terms: 7.5 + w = -4.609772229 Solving 7.5 + w = -4.609772229 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = -4.609772229 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -4.609772229 + -7.5 w = -4.609772229 + -7.5 Combine like terms: -4.609772229 + -7.5 = -12.109772229 w = -12.109772229 Simplifying w = -12.109772229Solution
The solution to the problem is based on the solutions from the subproblems. w = {-2.890227771, -12.109772229}
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