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Simplifying (w + 3) = 2w2 + 17w + 37 Reorder the terms: (3 + w) = 2w2 + 17w + 37 Remove parenthesis around (3 + w) 3 + w = 2w2 + 17w + 37 Reorder the terms: 3 + w = 37 + 17w + 2w2 Solving 3 + w = 37 + 17w + 2w2 Solving for variable 'w'. Reorder the terms: 3 + -37 + w + -17w + -2w2 = 37 + 17w + 2w2 + -37 + -17w + -2w2 Combine like terms: 3 + -37 = -34 -34 + w + -17w + -2w2 = 37 + 17w + 2w2 + -37 + -17w + -2w2 Combine like terms: w + -17w = -16w -34 + -16w + -2w2 = 37 + 17w + 2w2 + -37 + -17w + -2w2 Reorder the terms: -34 + -16w + -2w2 = 37 + -37 + 17w + -17w + 2w2 + -2w2 Combine like terms: 37 + -37 = 0 -34 + -16w + -2w2 = 0 + 17w + -17w + 2w2 + -2w2 -34 + -16w + -2w2 = 17w + -17w + 2w2 + -2w2 Combine like terms: 17w + -17w = 0 -34 + -16w + -2w2 = 0 + 2w2 + -2w2 -34 + -16w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -34 + -16w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(17 + 8w + w2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(17 + 8w + w2)' equal to zero and attempt to solve: Simplifying 17 + 8w + w2 = 0 Solving 17 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 8w + -17 + w2 = 0 + -17 Reorder the terms: 17 + -17 + 8w + w2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 8w + w2 = 0 + -17 8w + w2 = 0 + -17 Combine like terms: 0 + -17 = -17 8w + w2 = -17 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 = -17 + 16 Reorder the terms: 16 + 8w + w2 = -17 + 16 Combine like terms: -17 + 16 = -1 16 + 8w + w2 = -1 Factor a perfect square on the left side: (w + 4)(w + 4) = -1 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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