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Simplifying 20w2 + -16w + 48 = 0 Reorder the terms: 48 + -16w + 20w2 = 0 Solving 48 + -16w + 20w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(12 + -4w + 5w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(12 + -4w + 5w2)' equal to zero and attempt to solve: Simplifying 12 + -4w + 5w2 = 0 Solving 12 + -4w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -0.8w + w2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -0.8w + -2.4 + w2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -0.8w + w2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -0.8w + w2 = 0 + -2.4 -0.8w + w2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -0.8w + w2 = -2.4 The w term is -0.8w. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8w + 0.16 + w2 = -2.4 + 0.16 Reorder the terms: 0.16 + -0.8w + w2 = -2.4 + 0.16 Combine like terms: -2.4 + 0.16 = -2.24 0.16 + -0.8w + w2 = -2.24 Factor a perfect square on the left side: (w + -0.4)(w + -0.4) = -2.24 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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