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Simplifying 42w + 4w2 = 54 Solving 42w + 4w2 = 54 Solving for variable 'w'. Reorder the terms: -54 + 42w + 4w2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 42w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 21w + 2w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + 21w + 2w2)' equal to zero and attempt to solve: Simplifying -27 + 21w + 2w2 = 0 Solving -27 + 21w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 10.5w + w2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 10.5w + 13.5 + w2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 10.5w + w2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 10.5w + w2 = 0 + 13.5 10.5w + w2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 10.5w + w2 = 13.5 The w term is 10.5w. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5w + 27.5625 + w2 = 13.5 + 27.5625 Reorder the terms: 27.5625 + 10.5w + w2 = 13.5 + 27.5625 Combine like terms: 13.5 + 27.5625 = 41.0625 27.5625 + 10.5w + w2 = 41.0625 Factor a perfect square on the left side: (w + 5.25)(w + 5.25) = 41.0625 Calculate the square root of the right side: 6.408002809 Break this problem into two subproblems by setting (w + 5.25) equal to 6.408002809 and -6.408002809.Subproblem 1
w + 5.25 = 6.408002809 Simplifying w + 5.25 = 6.408002809 Reorder the terms: 5.25 + w = 6.408002809 Solving 5.25 + w = 6.408002809 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + w = 6.408002809 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + w = 6.408002809 + -5.25 w = 6.408002809 + -5.25 Combine like terms: 6.408002809 + -5.25 = 1.158002809 w = 1.158002809 Simplifying w = 1.158002809Subproblem 2
w + 5.25 = -6.408002809 Simplifying w + 5.25 = -6.408002809 Reorder the terms: 5.25 + w = -6.408002809 Solving 5.25 + w = -6.408002809 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + w = -6.408002809 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + w = -6.408002809 + -5.25 w = -6.408002809 + -5.25 Combine like terms: -6.408002809 + -5.25 = -11.658002809 w = -11.658002809 Simplifying w = -11.658002809Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.158002809, -11.658002809}Solution
w = {1.158002809, -11.658002809}
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