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Simplifying 2y * 2y * 2y + -5y * 5y + -3y = 0 Reorder the terms for easier multiplication: 2 * 2 * 2y * y * y + -5y * 5y + -3y = 0 Multiply 2 * 2 4 * 2y * y * y + -5y * 5y + -3y = 0 Multiply 4 * 2 8y * y * y + -5y * 5y + -3y = 0 Multiply y * y 8y2 * y + -5y * 5y + -3y = 0 Multiply y2 * y 8y3 + -5y * 5y + -3y = 0 Reorder the terms for easier multiplication: 8y3 + -5 * 5y * y + -3y = 0 Multiply -5 * 5 8y3 + -25y * y + -3y = 0 Multiply y * y 8y3 + -25y2 + -3y = 0 Reorder the terms: -3y + -25y2 + 8y3 = 0 Solving -3y + -25y2 + 8y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-3 + -25y + 8y2) = 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 '(-3 + -25y + 8y2)' equal to zero and attempt to solve: Simplifying -3 + -25y + 8y2 = 0 Solving -3 + -25y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -3.125y + y2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3.125y + 0.375 + y2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3.125y + y2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3.125y + y2 = 0 + 0.375 -3.125y + y2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3.125y + y2 = 0.375 The y term is -3.125y. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125y + 2.44140625 + y2 = 0.375 + 2.44140625 Reorder the terms: 2.44140625 + -3.125y + y2 = 0.375 + 2.44140625 Combine like terms: 0.375 + 2.44140625 = 2.81640625 2.44140625 + -3.125y + y2 = 2.81640625 Factor a perfect square on the left side: (y + -1.5625)(y + -1.5625) = 2.81640625 Calculate the square root of the right side: 1.678215198 Break this problem into two subproblems by setting (y + -1.5625) equal to 1.678215198 and -1.678215198.Subproblem 1
y + -1.5625 = 1.678215198 Simplifying y + -1.5625 = 1.678215198 Reorder the terms: -1.5625 + y = 1.678215198 Solving -1.5625 + y = 1.678215198 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + y = 1.678215198 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + y = 1.678215198 + 1.5625 y = 1.678215198 + 1.5625 Combine like terms: 1.678215198 + 1.5625 = 3.240715198 y = 3.240715198 Simplifying y = 3.240715198Subproblem 2
y + -1.5625 = -1.678215198 Simplifying y + -1.5625 = -1.678215198 Reorder the terms: -1.5625 + y = -1.678215198 Solving -1.5625 + y = -1.678215198 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + y = -1.678215198 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + y = -1.678215198 + 1.5625 y = -1.678215198 + 1.5625 Combine like terms: -1.678215198 + 1.5625 = -0.115715198 y = -0.115715198 Simplifying y = -0.115715198Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.240715198, -0.115715198}Solution
y = {0, 3.240715198, -0.115715198}
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