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Simplifying 15w3 + -35w2 + 110w = 0 Reorder the terms: 110w + -35w2 + 15w3 = 0 Solving 110w + -35w2 + 15w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5w'. 5w(22 + -7w + 3w2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(22 + -7w + 3w2)' equal to zero and attempt to solve: Simplifying 22 + -7w + 3w2 = 0 Solving 22 + -7w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.333333333 + -2.333333333w + w2 = 0 Move the constant term to the right: Add '-7.333333333' to each side of the equation. 7.333333333 + -2.333333333w + -7.333333333 + w2 = 0 + -7.333333333 Reorder the terms: 7.333333333 + -7.333333333 + -2.333333333w + w2 = 0 + -7.333333333 Combine like terms: 7.333333333 + -7.333333333 = 0.000000000 0.000000000 + -2.333333333w + w2 = 0 + -7.333333333 -2.333333333w + w2 = 0 + -7.333333333 Combine like terms: 0 + -7.333333333 = -7.333333333 -2.333333333w + w2 = -7.333333333 The w term is -2.333333333w. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333w + 1.361111112 + w2 = -7.333333333 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333w + w2 = -7.333333333 + 1.361111112 Combine like terms: -7.333333333 + 1.361111112 = -5.972222221 1.361111112 + -2.333333333w + w2 = -5.972222221 Factor a perfect square on the left side: (w + -1.166666667)(w + -1.166666667) = -5.972222221 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.Solution
w = {0}
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