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Simplifying 4w + -2w(1 + -1w) = -38 4w + (1 * -2w + -1w * -2w) = -38 4w + (-2w + 2w2) = -38 Combine like terms: 4w + -2w = 2w 2w + 2w2 = -38 Solving 2w + 2w2 = -38 Solving for variable 'w'. Reorder the terms: 38 + 2w + 2w2 = -38 + 38 Combine like terms: -38 + 38 = 0 38 + 2w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19 + w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + w + w2)' equal to zero and attempt to solve: Simplifying 19 + w + w2 = 0 Solving 19 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + w + -19 + w2 = 0 + -19 Reorder the terms: 19 + -19 + w + w2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + w + w2 = 0 + -19 w + w2 = 0 + -19 Combine like terms: 0 + -19 = -19 w + w2 = -19 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. w + 0.25 + w2 = -19 + 0.25 Reorder the terms: 0.25 + w + w2 = -19 + 0.25 Combine like terms: -19 + 0.25 = -18.75 0.25 + w + w2 = -18.75 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = -18.75 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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