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Simplifying 15w2 + -10w + 5 = 0 Reorder the terms: 5 + -10w + 15w2 = 0 Solving 5 + -10w + 15w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -2w + 3w2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -2w + 3w2)' equal to zero and attempt to solve: Simplifying 1 + -2w + 3w2 = 0 Solving 1 + -2w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -0.6666666667w + w2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.6666666667w + -0.3333333333 + w2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.6666666667w + w2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.6666666667w + w2 = 0 + -0.3333333333 -0.6666666667w + w2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.6666666667w + w2 = -0.3333333333 The w term is -0.6666666667w. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667w + 0.1111111112 + w2 = -0.3333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667w + w2 = -0.3333333333 + 0.1111111112 Combine like terms: -0.3333333333 + 0.1111111112 = -0.2222222221 0.1111111112 + -0.6666666667w + w2 = -0.2222222221 Factor a perfect square on the left side: (w + -0.3333333334)(w + -0.3333333334) = -0.2222222221 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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