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Simplifying 20w2 + 10w + 40 = 0 Reorder the terms: 40 + 10w + 20w2 = 0 Solving 40 + 10w + 20w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '10'. 10(4 + w + 2w2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(4 + w + 2w2)' equal to zero and attempt to solve: Simplifying 4 + w + 2w2 = 0 Solving 4 + w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 0.5w + w2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.5w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + 0.5w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.5w + w2 = 0 + -2 0.5w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.5w + w2 = -2 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5w + 0.25 + w2 = -2 + 0.25 Reorder the terms: 0.25 + 0.5w + w2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + 0.5w + w2 = -1.75 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = -1.75 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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