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Simplifying 30w2 + 33w + 90 = 0 Reorder the terms: 90 + 33w + 30w2 = 0 Solving 90 + 33w + 30w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(30 + 11w + 10w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(30 + 11w + 10w2)' equal to zero and attempt to solve: Simplifying 30 + 11w + 10w2 = 0 Solving 30 + 11w + 10w2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 3 + 1.1w + w2 = 0.0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1.1w + -3 + w2 = 0.0 + -3 Reorder the terms: 3 + -3 + 1.1w + w2 = 0.0 + -3 Combine like terms: 3 + -3 = 0 0 + 1.1w + w2 = 0.0 + -3 1.1w + w2 = 0.0 + -3 Combine like terms: 0.0 + -3 = -3 1.1w + w2 = -3 The w term is 1.1w. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1w + 0.3025 + w2 = -3 + 0.3025 Reorder the terms: 0.3025 + 1.1w + w2 = -3 + 0.3025 Combine like terms: -3 + 0.3025 = -2.6975 0.3025 + 1.1w + w2 = -2.6975 Factor a perfect square on the left side: (w + 0.55)(w + 0.55) = -2.6975 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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