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Simplifying -4w2 + 32w + -84 = 0 Reorder the terms: -84 + 32w + -4w2 = 0 Solving -84 + 32w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 8w + -1w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + 8w + -1w2)' equal to zero and attempt to solve: Simplifying -21 + 8w + -1w2 = 0 Solving -21 + 8w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 21 + -8w + w2 = 0 Move the constant term to the right: Add '-21' to each side of the equation. 21 + -8w + -21 + w2 = 0 + -21 Reorder the terms: 21 + -21 + -8w + w2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -8w + w2 = 0 + -21 -8w + w2 = 0 + -21 Combine like terms: 0 + -21 = -21 -8w + w2 = -21 The w term is -8w. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8w + 16 + w2 = -21 + 16 Reorder the terms: 16 + -8w + w2 = -21 + 16 Combine like terms: -21 + 16 = -5 16 + -8w + w2 = -5 Factor a perfect square on the left side: (w + -4)(w + -4) = -5 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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