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Simplifying 4y3 + -44y2 + -9y = 0 Reorder the terms: -9y + -44y2 + 4y3 = 0 Solving -9y + -44y2 + 4y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-9 + -44y + 4y2) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(-9 + -44y + 4y2)' equal to zero and attempt to solve: Simplifying -9 + -44y + 4y2 = 0 Solving -9 + -44y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -11y + y2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -11y + 2.25 + y2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -11y + y2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -11y + y2 = 0 + 2.25 -11y + y2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -11y + y2 = 2.25 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = 2.25 + 30.25 Reorder the terms: 30.25 + -11y + y2 = 2.25 + 30.25 Combine like terms: 2.25 + 30.25 = 32.5 30.25 + -11y + y2 = 32.5 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 32.5 Calculate the square root of the right side: 5.700877125 Break this problem into two subproblems by setting (y + -5.5) equal to 5.700877125 and -5.700877125.Subproblem 1
y + -5.5 = 5.700877125 Simplifying y + -5.5 = 5.700877125 Reorder the terms: -5.5 + y = 5.700877125 Solving -5.5 + y = 5.700877125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 5.700877125 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 5.700877125 + 5.5 y = 5.700877125 + 5.5 Combine like terms: 5.700877125 + 5.5 = 11.200877125 y = 11.200877125 Simplifying y = 11.200877125Subproblem 2
y + -5.5 = -5.700877125 Simplifying y + -5.5 = -5.700877125 Reorder the terms: -5.5 + y = -5.700877125 Solving -5.5 + y = -5.700877125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -5.700877125 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -5.700877125 + 5.5 y = -5.700877125 + 5.5 Combine like terms: -5.700877125 + 5.5 = -0.200877125 y = -0.200877125 Simplifying y = -0.200877125Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.200877125, -0.200877125}Solution
y = {0, 11.200877125, -0.200877125}
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