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Simplifying (18w2 + -6w + 14) + (12w + -8) = 0 Reorder the terms: (14 + -6w + 18w2) + (12w + -8) = 0 Remove parenthesis around (14 + -6w + 18w2) 14 + -6w + 18w2 + (12w + -8) = 0 Reorder the terms: 14 + -6w + 18w2 + (-8 + 12w) = 0 Remove parenthesis around (-8 + 12w) 14 + -6w + 18w2 + -8 + 12w = 0 Reorder the terms: 14 + -8 + -6w + 12w + 18w2 = 0 Combine like terms: 14 + -8 = 6 6 + -6w + 12w + 18w2 = 0 Combine like terms: -6w + 12w = 6w 6 + 6w + 18w2 = 0 Solving 6 + 6w + 18w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '6'. 6(1 + w + 3w2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + w + 3w2)' equal to zero and attempt to solve: Simplifying 1 + w + 3w2 = 0 Solving 1 + w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 0.3333333333w + w2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.3333333333w + -0.3333333333 + w2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.3333333333w + w2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.3333333333w + w2 = 0 + -0.3333333333 0.3333333333w + w2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.3333333333w + w2 = -0.3333333333 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. 0.3333333333w + 0.25 + w2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333w + w2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + 0.3333333333w + w2 = -0.0833333333 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = -0.0833333333 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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