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Simplifying 2w2 + -6w = 12w + -48 Reorder the terms: -6w + 2w2 = 12w + -48 Reorder the terms: -6w + 2w2 = -48 + 12w Solving -6w + 2w2 = -48 + 12w Solving for variable 'w'. Reorder the terms: 48 + -6w + -12w + 2w2 = -48 + 12w + 48 + -12w Combine like terms: -6w + -12w = -18w 48 + -18w + 2w2 = -48 + 12w + 48 + -12w Reorder the terms: 48 + -18w + 2w2 = -48 + 48 + 12w + -12w Combine like terms: -48 + 48 = 0 48 + -18w + 2w2 = 0 + 12w + -12w 48 + -18w + 2w2 = 12w + -12w Combine like terms: 12w + -12w = 0 48 + -18w + 2w2 = 0 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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