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Simplifying (w + -1) = 2w2 + 6w + 16 Reorder the terms: (-1 + w) = 2w2 + 6w + 16 Remove parenthesis around (-1 + w) -1 + w = 2w2 + 6w + 16 Reorder the terms: -1 + w = 16 + 6w + 2w2 Solving -1 + w = 16 + 6w + 2w2 Solving for variable 'w'. Reorder the terms: -1 + -16 + w + -6w + -2w2 = 16 + 6w + 2w2 + -16 + -6w + -2w2 Combine like terms: -1 + -16 = -17 -17 + w + -6w + -2w2 = 16 + 6w + 2w2 + -16 + -6w + -2w2 Combine like terms: w + -6w = -5w -17 + -5w + -2w2 = 16 + 6w + 2w2 + -16 + -6w + -2w2 Reorder the terms: -17 + -5w + -2w2 = 16 + -16 + 6w + -6w + 2w2 + -2w2 Combine like terms: 16 + -16 = 0 -17 + -5w + -2w2 = 0 + 6w + -6w + 2w2 + -2w2 -17 + -5w + -2w2 = 6w + -6w + 2w2 + -2w2 Combine like terms: 6w + -6w = 0 -17 + -5w + -2w2 = 0 + 2w2 + -2w2 -17 + -5w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -17 + -5w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 5w + 2w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 5w + 2w2)' equal to zero and attempt to solve: Simplifying 17 + 5w + 2w2 = 0 Solving 17 + 5w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + 2.5w + w2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 2.5w + -8.5 + w2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 2.5w + w2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 2.5w + w2 = 0 + -8.5 2.5w + w2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 2.5w + w2 = -8.5 The w term is 2.5w. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5w + 1.5625 + w2 = -8.5 + 1.5625 Reorder the terms: 1.5625 + 2.5w + w2 = -8.5 + 1.5625 Combine like terms: -8.5 + 1.5625 = -6.9375 1.5625 + 2.5w + w2 = -6.9375 Factor a perfect square on the left side: (w + 1.25)(w + 1.25) = -6.9375 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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