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Simplifying 8w2 + 24w + 216 = 0 Reorder the terms: 216 + 24w + 8w2 = 0 Solving 216 + 24w + 8w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '8'. 8(27 + 3w + w2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(27 + 3w + w2)' equal to zero and attempt to solve: Simplifying 27 + 3w + w2 = 0 Solving 27 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 3w + -27 + w2 = 0 + -27 Reorder the terms: 27 + -27 + 3w + w2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 3w + w2 = 0 + -27 3w + w2 = 0 + -27 Combine like terms: 0 + -27 = -27 3w + w2 = -27 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = -27 + 2.25 Reorder the terms: 2.25 + 3w + w2 = -27 + 2.25 Combine like terms: -27 + 2.25 = -24.75 2.25 + 3w + w2 = -24.75 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = -24.75 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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