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Simplifying 18w4 + 10w2 + 50 = 0 Reorder the terms: 50 + 10w2 + 18w4 = 0 Solving 50 + 10w2 + 18w4 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 5w2 + 9w4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 5w2 + 9w4)' equal to zero and attempt to solve: Simplifying 25 + 5w2 + 9w4 = 0 Solving 25 + 5w2 + 9w4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.777777778 + 0.5555555556w2 + w4 = 0 Move the constant term to the right: Add '-2.777777778' to each side of the equation. 2.777777778 + 0.5555555556w2 + -2.777777778 + w4 = 0 + -2.777777778 Reorder the terms: 2.777777778 + -2.777777778 + 0.5555555556w2 + w4 = 0 + -2.777777778 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 0.000000000 + 0.5555555556w2 + w4 = 0 + -2.777777778 0.5555555556w2 + w4 = 0 + -2.777777778 Combine like terms: 0 + -2.777777778 = -2.777777778 0.5555555556w2 + w4 = -2.777777778 The w term is 0.5555555556w2. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556w2 + 0.07716049384 + w4 = -2.777777778 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556w2 + w4 = -2.777777778 + 0.07716049384 Combine like terms: -2.777777778 + 0.07716049384 = -2.70061728416 0.07716049384 + 0.5555555556w2 + w4 = -2.70061728416 Factor a perfect square on the left side: (w2 + 0.2777777778)(w2 + 0.2777777778) = -2.70061728416 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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