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Simplifying 27y8 + 81y5 + 90y2 = 0 Reorder the terms: 90y2 + 81y5 + 27y8 = 0 Solving 90y2 + 81y5 + 27y8 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '9y2'. 9y2(10 + 9y3 + 3y6) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(10 + 9y3 + 3y6)' equal to zero and attempt to solve: Simplifying 10 + 9y3 + 3y6 = 0 Solving 10 + 9y3 + 3y6 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + 3y3 + y6 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 3y3 + -3.333333333 + y6 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 3y3 + y6 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 3y3 + y6 = 0 + -3.333333333 3y3 + y6 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 3y3 + y6 = -3.333333333 The y term is 3y3. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y3 + 2.25 + y6 = -3.333333333 + 2.25 Reorder the terms: 2.25 + 3y3 + y6 = -3.333333333 + 2.25 Combine like terms: -3.333333333 + 2.25 = -1.083333333 2.25 + 3y3 + y6 = -1.083333333 Factor a perfect square on the left side: (y3 + 1.5)(y3 + 1.5) = -1.083333333 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
y = {0}
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