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Simplifying 4w2 + -28w + 62 = 0 Reorder the terms: 62 + -28w + 4w2 = 0 Solving 62 + -28w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(31 + -14w + 2w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + -14w + 2w2)' equal to zero and attempt to solve: Simplifying 31 + -14w + 2w2 = 0 Solving 31 + -14w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15.5 + -7w + w2 = 0 Move the constant term to the right: Add '-15.5' to each side of the equation. 15.5 + -7w + -15.5 + w2 = 0 + -15.5 Reorder the terms: 15.5 + -15.5 + -7w + w2 = 0 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + -7w + w2 = 0 + -15.5 -7w + w2 = 0 + -15.5 Combine like terms: 0 + -15.5 = -15.5 -7w + w2 = -15.5 The w term is -7w. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7w + 12.25 + w2 = -15.5 + 12.25 Reorder the terms: 12.25 + -7w + w2 = -15.5 + 12.25 Combine like terms: -15.5 + 12.25 = -3.25 12.25 + -7w + w2 = -3.25 Factor a perfect square on the left side: (w + -3.5)(w + -3.5) = -3.25 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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