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Simplifying 4w2 + 32w + 220 = 0 Reorder the terms: 220 + 32w + 4w2 = 0 Solving 220 + 32w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(55 + 8w + w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(55 + 8w + w2)' equal to zero and attempt to solve: Simplifying 55 + 8w + w2 = 0 Solving 55 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + 8w + -55 + w2 = 0 + -55 Reorder the terms: 55 + -55 + 8w + w2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + 8w + w2 = 0 + -55 8w + w2 = 0 + -55 Combine like terms: 0 + -55 = -55 8w + w2 = -55 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 = -55 + 16 Reorder the terms: 16 + 8w + w2 = -55 + 16 Combine like terms: -55 + 16 = -39 16 + 8w + w2 = -39 Factor a perfect square on the left side: (w + 4)(w + 4) = -39 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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