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Simplifying 8(2w + -1) * 4w = -116 Reorder the terms: 8(-1 + 2w) * 4w = -116 Reorder the terms for easier multiplication: 8 * 4w(-1 + 2w) = -116 Multiply 8 * 4 32w(-1 + 2w) = -116 (-1 * 32w + 2w * 32w) = -116 (-32w + 64w2) = -116 Solving -32w + 64w2 = -116 Solving for variable 'w'. Reorder the terms: 116 + -32w + 64w2 = -116 + 116 Combine like terms: -116 + 116 = 0 116 + -32w + 64w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(29 + -8w + 16w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(29 + -8w + 16w2)' equal to zero and attempt to solve: Simplifying 29 + -8w + 16w2 = 0 Solving 29 + -8w + 16w2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.8125 + -0.5w + w2 = 0 Move the constant term to the right: Add '-1.8125' to each side of the equation. 1.8125 + -0.5w + -1.8125 + w2 = 0 + -1.8125 Reorder the terms: 1.8125 + -1.8125 + -0.5w + w2 = 0 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + -0.5w + w2 = 0 + -1.8125 -0.5w + w2 = 0 + -1.8125 Combine like terms: 0 + -1.8125 = -1.8125 -0.5w + w2 = -1.8125 The w term is -0.5w. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5w + 0.0625 + w2 = -1.8125 + 0.0625 Reorder the terms: 0.0625 + -0.5w + w2 = -1.8125 + 0.0625 Combine like terms: -1.8125 + 0.0625 = -1.75 0.0625 + -0.5w + w2 = -1.75 Factor a perfect square on the left side: (w + -0.25)(w + -0.25) = -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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