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Simplifying 7w + -3w(4w + 8) = 11 Reorder the terms: 7w + -3w(8 + 4w) = 11 7w + (8 * -3w + 4w * -3w) = 11 7w + (-24w + -12w2) = 11 Combine like terms: 7w + -24w = -17w -17w + -12w2 = 11 Solving -17w + -12w2 = 11 Solving for variable 'w'. Reorder the terms: -11 + -17w + -12w2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -17w + -12w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 17w + 12w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 17w + 12w2)' equal to zero and attempt to solve: Simplifying 11 + 17w + 12w2 = 0 Solving 11 + 17w + 12w2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.9166666667 + 1.416666667w + w2 = 0 Move the constant term to the right: Add '-0.9166666667' to each side of the equation. 0.9166666667 + 1.416666667w + -0.9166666667 + w2 = 0 + -0.9166666667 Reorder the terms: 0.9166666667 + -0.9166666667 + 1.416666667w + w2 = 0 + -0.9166666667 Combine like terms: 0.9166666667 + -0.9166666667 = 0.0000000000 0.0000000000 + 1.416666667w + w2 = 0 + -0.9166666667 1.416666667w + w2 = 0 + -0.9166666667 Combine like terms: 0 + -0.9166666667 = -0.9166666667 1.416666667w + w2 = -0.9166666667 The w term is 1.416666667w. Take half its coefficient (0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. 1.416666667w + 0.5017361113 + w2 = -0.9166666667 + 0.5017361113 Reorder the terms: 0.5017361113 + 1.416666667w + w2 = -0.9166666667 + 0.5017361113 Combine like terms: -0.9166666667 + 0.5017361113 = -0.4149305554 0.5017361113 + 1.416666667w + w2 = -0.4149305554 Factor a perfect square on the left side: (w + 0.7083333335)(w + 0.7083333335) = -0.4149305554 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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