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Simplifying 2w2 + 10w + 15w3 = 0 Reorder the terms: 10w + 2w2 + 15w3 = 0 Solving 10w + 2w2 + 15w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(10 + 2w + 15w2) = 0Subproblem 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 '(10 + 2w + 15w2)' equal to zero and attempt to solve: Simplifying 10 + 2w + 15w2 = 0 Solving 10 + 2w + 15w2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.6666666667 + 0.1333333333w + w2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 0.1333333333w + -0.6666666667 + w2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 0.1333333333w + w2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 0.1333333333w + w2 = 0 + -0.6666666667 0.1333333333w + w2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 0.1333333333w + w2 = -0.6666666667 The w term is 0.1333333333w. Take half its coefficient (0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. 0.1333333333w + 0.004444444442 + w2 = -0.6666666667 + 0.004444444442 Reorder the terms: 0.004444444442 + 0.1333333333w + w2 = -0.6666666667 + 0.004444444442 Combine like terms: -0.6666666667 + 0.004444444442 = -0.662222222258 0.004444444442 + 0.1333333333w + w2 = -0.662222222258 Factor a perfect square on the left side: (w + 0.06666666665)(w + 0.06666666665) = -0.662222222258 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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