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Simplifying (w + 6) = 2w2 + 2w + 60 Reorder the terms: (6 + w) = 2w2 + 2w + 60 Remove parenthesis around (6 + w) 6 + w = 2w2 + 2w + 60 Reorder the terms: 6 + w = 60 + 2w + 2w2 Solving 6 + w = 60 + 2w + 2w2 Solving for variable 'w'. Reorder the terms: 6 + -60 + w + -2w + -2w2 = 60 + 2w + 2w2 + -60 + -2w + -2w2 Combine like terms: 6 + -60 = -54 -54 + w + -2w + -2w2 = 60 + 2w + 2w2 + -60 + -2w + -2w2 Combine like terms: w + -2w = -1w -54 + -1w + -2w2 = 60 + 2w + 2w2 + -60 + -2w + -2w2 Reorder the terms: -54 + -1w + -2w2 = 60 + -60 + 2w + -2w + 2w2 + -2w2 Combine like terms: 60 + -60 = 0 -54 + -1w + -2w2 = 0 + 2w + -2w + 2w2 + -2w2 -54 + -1w + -2w2 = 2w + -2w + 2w2 + -2w2 Combine like terms: 2w + -2w = 0 -54 + -1w + -2w2 = 0 + 2w2 + -2w2 -54 + -1w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -54 + -1w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(54 + w + 2w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(54 + w + 2w2)' equal to zero and attempt to solve: Simplifying 54 + w + 2w2 = 0 Solving 54 + w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 27 + 0.5w + w2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + 0.5w + -27 + w2 = 0 + -27 Reorder the terms: 27 + -27 + 0.5w + w2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 0.5w + w2 = 0 + -27 0.5w + w2 = 0 + -27 Combine like terms: 0 + -27 = -27 0.5w + w2 = -27 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5w + 0.25 + w2 = -27 + 0.25 Reorder the terms: 0.25 + 0.5w + w2 = -27 + 0.25 Combine like terms: -27 + 0.25 = -26.75 0.25 + 0.5w + w2 = -26.75 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = -26.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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