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Simplifying 2w2 + -18w + 48 = 0 Reorder the terms: 48 + -18w + 2w2 = 0 Solving 48 + -18w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + -9w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -9w + w2)' equal to zero and attempt to solve: Simplifying 24 + -9w + w2 = 0 Solving 24 + -9w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -9w + -24 + w2 = 0 + -24 Reorder the terms: 24 + -24 + -9w + w2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -9w + w2 = 0 + -24 -9w + w2 = 0 + -24 Combine like terms: 0 + -24 = -24 -9w + w2 = -24 The w term is -9w. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9w + 20.25 + w2 = -24 + 20.25 Reorder the terms: 20.25 + -9w + w2 = -24 + 20.25 Combine like terms: -24 + 20.25 = -3.75 20.25 + -9w + w2 = -3.75 Factor a perfect square on the left side: (w + -4.5)(w + -4.5) = -3.75 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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