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Simplifying -16w2 + -16w + -100 = 0 Reorder the terms: -100 + -16w + -16w2 = 0 Solving -100 + -16w + -16w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-4'. -4(25 + 4w + 4w2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(25 + 4w + 4w2)' equal to zero and attempt to solve: Simplifying 25 + 4w + 4w2 = 0 Solving 25 + 4w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + w + w2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + w + -6.25 + w2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + w + w2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + w + w2 = 0 + -6.25 w + w2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 w + w2 = -6.25 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. + 0.25 + w2 = -6.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + w2 = -6.25 + 0.25 Combine like terms: -6.25 + 0.25 = -6 1.25 + w2 = -6 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = -6 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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