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Simplifying -20w2 + -13w = 15 Reorder the terms: -13w + -20w2 = 15 Solving -13w + -20w2 = 15 Solving for variable 'w'. Reorder the terms: -15 + -13w + -20w2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -13w + -20w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 13w + 20w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 13w + 20w2)' equal to zero and attempt to solve: Simplifying 15 + 13w + 20w2 = 0 Solving 15 + 13w + 20w2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.75 + 0.65w + w2 = 0.0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.65w + -0.75 + w2 = 0.0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.65w + w2 = 0.0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.65w + w2 = 0.0 + -0.75 0.65w + w2 = 0.0 + -0.75 Combine like terms: 0.0 + -0.75 = -0.75 0.65w + w2 = -0.75 The w term is 0.65w. Take half its coefficient (0.325). Square it (0.105625) and add it to both sides. Add '0.105625' to each side of the equation. 0.65w + 0.105625 + w2 = -0.75 + 0.105625 Reorder the terms: 0.105625 + 0.65w + w2 = -0.75 + 0.105625 Combine like terms: -0.75 + 0.105625 = -0.644375 0.105625 + 0.65w + w2 = -0.644375 Factor a perfect square on the left side: (w + 0.325)(w + 0.325) = -0.644375 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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