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Simplifying 6w5 + 14w4 + 10w3 = 0 Reorder the terms: 10w3 + 14w4 + 6w5 = 0 Solving 10w3 + 14w4 + 6w5 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w3'. 2w3(5 + 7w + 3w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'w3' equal to zero and attempt to solve: Simplifying w3 = 0 Solving w3 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + 7w + 3w2)' equal to zero and attempt to solve: Simplifying 5 + 7w + 3w2 = 0 Solving 5 + 7w + 3w2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 2.333333333w + w2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 2.333333333w + -1.666666667 + w2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 2.333333333w + w2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 2.333333333w + w2 = 0 + -1.666666667 2.333333333w + w2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 2.333333333w + w2 = -1.666666667 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 = -1.666666667 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333w + w2 = -1.666666667 + 1.361111112 Combine like terms: -1.666666667 + 1.361111112 = -0.305555555 1.361111112 + 2.333333333w + w2 = -0.305555555 Factor a perfect square on the left side: (w + 1.166666667)(w + 1.166666667) = -0.305555555 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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