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Simplifying 27w + 60 = 3w2 Reorder the terms: 60 + 27w = 3w2 Solving 60 + 27w = 3w2 Solving for variable 'w'. Combine like terms: 3w2 + -3w2 = 0 60 + 27w + -3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(20 + 9w + -1w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(20 + 9w + -1w2)' equal to zero and attempt to solve: Simplifying 20 + 9w + -1w2 = 0 Solving 20 + 9w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -9w + w2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -9w + 20 + w2 = 0 + 20 Reorder the terms: -20 + 20 + -9w + w2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -9w + w2 = 0 + 20 -9w + w2 = 0 + 20 Combine like terms: 0 + 20 = 20 -9w + w2 = 20 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 = 20 + 20.25 Reorder the terms: 20.25 + -9w + w2 = 20 + 20.25 Combine like terms: 20 + 20.25 = 40.25 20.25 + -9w + w2 = 40.25 Factor a perfect square on the left side: (w + -4.5)(w + -4.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (w + -4.5) equal to 6.34428877 and -6.34428877.Subproblem 1
w + -4.5 = 6.34428877 Simplifying w + -4.5 = 6.34428877 Reorder the terms: -4.5 + w = 6.34428877 Solving -4.5 + w = 6.34428877 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 = 6.34428877 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = 6.34428877 + 4.5 w = 6.34428877 + 4.5 Combine like terms: 6.34428877 + 4.5 = 10.84428877 w = 10.84428877 Simplifying w = 10.84428877Subproblem 2
w + -4.5 = -6.34428877 Simplifying w + -4.5 = -6.34428877 Reorder the terms: -4.5 + w = -6.34428877 Solving -4.5 + w = -6.34428877 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 = -6.34428877 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = -6.34428877 + 4.5 w = -6.34428877 + 4.5 Combine like terms: -6.34428877 + 4.5 = -1.84428877 w = -1.84428877 Simplifying w = -1.84428877Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.84428877, -1.84428877}Solution
w = {10.84428877, -1.84428877}
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