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Simplifying 30w3 = 25w2 + -105w Reorder the terms: 30w3 = -105w + 25w2 Solving 30w3 = -105w + 25w2 Solving for variable 'w'. Reorder the terms: 105w + -25w2 + 30w3 = -105w + 25w2 + 105w + -25w2 Reorder the terms: 105w + -25w2 + 30w3 = -105w + 105w + 25w2 + -25w2 Combine like terms: -105w + 105w = 0 105w + -25w2 + 30w3 = 0 + 25w2 + -25w2 105w + -25w2 + 30w3 = 25w2 + -25w2 Combine like terms: 25w2 + -25w2 = 0 105w + -25w2 + 30w3 = 0 Factor out the Greatest Common Factor (GCF), '5w'. 5w(21 + -5w + 6w2) = 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 '(21 + -5w + 6w2)' equal to zero and attempt to solve: Simplifying 21 + -5w + 6w2 = 0 Solving 21 + -5w + 6w2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.5 + -0.8333333333w + w2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -0.8333333333w + -3.5 + w2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -0.8333333333w + w2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -0.8333333333w + w2 = 0 + -3.5 -0.8333333333w + w2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -0.8333333333w + w2 = -3.5 The w term is -0.8333333333w. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333w + 0.1736111111 + w2 = -3.5 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333w + w2 = -3.5 + 0.1736111111 Combine like terms: -3.5 + 0.1736111111 = -3.3263888889 0.1736111111 + -0.8333333333w + w2 = -3.3263888889 Factor a perfect square on the left side: (w + -0.4166666667)(w + -0.4166666667) = -3.3263888889 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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