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Simplifying 0 = w2 + 8w + 480 Reorder the terms: 0 = 480 + 8w + w2 Solving 0 = 480 + 8w + w2 Solving for variable 'w'. Combine like terms: 0 + -480 = -480 -480 + -8w + -1w2 = 480 + 8w + w2 + -480 + -8w + -1w2 Reorder the terms: -480 + -8w + -1w2 = 480 + -480 + 8w + -8w + w2 + -1w2 Combine like terms: 480 + -480 = 0 -480 + -8w + -1w2 = 0 + 8w + -8w + w2 + -1w2 -480 + -8w + -1w2 = 8w + -8w + w2 + -1w2 Combine like terms: 8w + -8w = 0 -480 + -8w + -1w2 = 0 + w2 + -1w2 -480 + -8w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -480 + -8w + -1w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(480 + 8w + w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(480 + 8w + w2)' equal to zero and attempt to solve: Simplifying 480 + 8w + w2 = 0 Solving 480 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-480' to each side of the equation. 480 + 8w + -480 + w2 = 0 + -480 Reorder the terms: 480 + -480 + 8w + w2 = 0 + -480 Combine like terms: 480 + -480 = 0 0 + 8w + w2 = 0 + -480 8w + w2 = 0 + -480 Combine like terms: 0 + -480 = -480 8w + w2 = -480 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 = -480 + 16 Reorder the terms: 16 + 8w + w2 = -480 + 16 Combine like terms: -480 + 16 = -464 16 + 8w + w2 = -464 Factor a perfect square on the left side: (w + 4)(w + 4) = -464 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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