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Simplifying -13w2 = 14w + 5 Reorder the terms: -13w2 = 5 + 14w Solving -13w2 = 5 + 14w Solving for variable 'w'. Reorder the terms: -5 + -14w + -13w2 = 5 + 14w + -5 + -14w Reorder the terms: -5 + -14w + -13w2 = 5 + -5 + 14w + -14w Combine like terms: 5 + -5 = 0 -5 + -14w + -13w2 = 0 + 14w + -14w -5 + -14w + -13w2 = 14w + -14w Combine like terms: 14w + -14w = 0 -5 + -14w + -13w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 14w + 13w2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 14w + 13w2)' equal to zero and attempt to solve: Simplifying 5 + 14w + 13w2 = 0 Solving 5 + 14w + 13w2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.3846153846 + 1.076923077w + w2 = 0 Move the constant term to the right: Add '-0.3846153846' to each side of the equation. 0.3846153846 + 1.076923077w + -0.3846153846 + w2 = 0 + -0.3846153846 Reorder the terms: 0.3846153846 + -0.3846153846 + 1.076923077w + w2 = 0 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + 1.076923077w + w2 = 0 + -0.3846153846 1.076923077w + w2 = 0 + -0.3846153846 Combine like terms: 0 + -0.3846153846 = -0.3846153846 1.076923077w + w2 = -0.3846153846 The w term is 1.076923077w. Take half its coefficient (0.5384615385). Square it (0.2899408284) and add it to both sides. Add '0.2899408284' to each side of the equation. 1.076923077w + 0.2899408284 + w2 = -0.3846153846 + 0.2899408284 Reorder the terms: 0.2899408284 + 1.076923077w + w2 = -0.3846153846 + 0.2899408284 Combine like terms: -0.3846153846 + 0.2899408284 = -0.0946745562 0.2899408284 + 1.076923077w + w2 = -0.0946745562 Factor a perfect square on the left side: (w + 0.5384615385)(w + 0.5384615385) = -0.0946745562 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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