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Simplifying 54y4 + 48y3 + 30y2 = 0 Reorder the terms: 30y2 + 48y3 + 54y4 = 0 Solving 30y2 + 48y3 + 54y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '6y2'. 6y2(5 + 8y + 9y2) = 0 Ignore the factor 6.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 '(5 + 8y + 9y2)' equal to zero and attempt to solve: Simplifying 5 + 8y + 9y2 = 0 Solving 5 + 8y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + 0.8888888889y + y2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + 0.8888888889y + -0.5555555556 + y2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + 0.8888888889y + y2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + 0.8888888889y + y2 = 0 + -0.5555555556 0.8888888889y + y2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 0.8888888889y + y2 = -0.5555555556 The y term is 0.8888888889y. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889y + 0.1975308642 + y2 = -0.5555555556 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889y + y2 = -0.5555555556 + 0.1975308642 Combine like terms: -0.5555555556 + 0.1975308642 = -0.3580246914 0.1975308642 + 0.8888888889y + y2 = -0.3580246914 Factor a perfect square on the left side: (y + 0.4444444445)(y + 0.4444444445) = -0.3580246914 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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