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Simplifying 2y3 + -23y2 + -7y = 0 Reorder the terms: -7y + -23y2 + 2y3 = 0 Solving -7y + -23y2 + 2y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-7 + -23y + 2y2) = 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 '(-7 + -23y + 2y2)' equal to zero and attempt to solve: Simplifying -7 + -23y + 2y2 = 0 Solving -7 + -23y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -11.5y + y2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -11.5y + 3.5 + y2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -11.5y + y2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -11.5y + y2 = 0 + 3.5 -11.5y + y2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -11.5y + y2 = 3.5 The y term is -11.5y. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5y + 33.0625 + y2 = 3.5 + 33.0625 Reorder the terms: 33.0625 + -11.5y + y2 = 3.5 + 33.0625 Combine like terms: 3.5 + 33.0625 = 36.5625 33.0625 + -11.5y + y2 = 36.5625 Factor a perfect square on the left side: (y + -5.75)(y + -5.75) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (y + -5.75) equal to 6.046693311 and -6.046693311.Subproblem 1
y + -5.75 = 6.046693311 Simplifying y + -5.75 = 6.046693311 Reorder the terms: -5.75 + y = 6.046693311 Solving -5.75 + y = 6.046693311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + y = 6.046693311 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + y = 6.046693311 + 5.75 y = 6.046693311 + 5.75 Combine like terms: 6.046693311 + 5.75 = 11.796693311 y = 11.796693311 Simplifying y = 11.796693311Subproblem 2
y + -5.75 = -6.046693311 Simplifying y + -5.75 = -6.046693311 Reorder the terms: -5.75 + y = -6.046693311 Solving -5.75 + y = -6.046693311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + y = -6.046693311 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + y = -6.046693311 + 5.75 y = -6.046693311 + 5.75 Combine like terms: -6.046693311 + 5.75 = -0.296693311 y = -0.296693311 Simplifying y = -0.296693311Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.796693311, -0.296693311}Solution
y = {0, 11.796693311, -0.296693311}
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