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Simplifying -24 = -6w + 2w(w + 2) Reorder the terms: -24 = -6w + 2w(2 + w) -24 = -6w + (2 * 2w + w * 2w) -24 = -6w + (4w + 2w2) Combine like terms: -6w + 4w = -2w -24 = -2w + 2w2 Solving -24 = -2w + 2w2 Solving for variable 'w'. Reorder the terms: -24 + 2w + -2w2 = -2w + 2w + 2w2 + -2w2 Combine like terms: -2w + 2w = 0 -24 + 2w + -2w2 = 0 + 2w2 + -2w2 -24 + 2w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -24 + 2w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + w + -1w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + w + -1w2)' equal to zero and attempt to solve: Simplifying -12 + w + -1w2 = 0 Solving -12 + w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -1w + w2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -1w + -12 + w2 = 0 + -12 Reorder the terms: 12 + -12 + -1w + w2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1w + w2 = 0 + -12 -1w + w2 = 0 + -12 Combine like terms: 0 + -12 = -12 -1w + w2 = -12 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. -1w + 0.25 + w2 = -12 + 0.25 Reorder the terms: 0.25 + -1w + w2 = -12 + 0.25 Combine like terms: -12 + 0.25 = -11.75 0.25 + -1w + w2 = -11.75 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = -11.75 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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