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Simplifying (-8y2 + -9y) + (8y3 + 9y2 + -2y) = 0 Reorder the terms: (-9y + -8y2) + (8y3 + 9y2 + -2y) = 0 Remove parenthesis around (-9y + -8y2) -9y + -8y2 + (8y3 + 9y2 + -2y) = 0 Reorder the terms: -9y + -8y2 + (-2y + 9y2 + 8y3) = 0 Remove parenthesis around (-2y + 9y2 + 8y3) -9y + -8y2 + -2y + 9y2 + 8y3 = 0 Reorder the terms: -9y + -2y + -8y2 + 9y2 + 8y3 = 0 Combine like terms: -9y + -2y = -11y -11y + -8y2 + 9y2 + 8y3 = 0 Combine like terms: -8y2 + 9y2 = 1y2 -11y + 1y2 + 8y3 = 0 Solving -11y + 1y2 + 8y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-11 + y + 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 '(-11 + y + 8y2)' equal to zero and attempt to solve: Simplifying -11 + y + 8y2 = 0 Solving -11 + y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + 0.125y + y2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 0.125y + 1.375 + y2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 0.125y + y2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 0.125y + y2 = 0 + 1.375 0.125y + y2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 0.125y + y2 = 1.375 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125y + 0.25 + y2 = 1.375 + 0.25 Reorder the terms: 0.25 + 0.125y + y2 = 1.375 + 0.25 Combine like terms: 1.375 + 0.25 = 1.625 0.25 + 0.125y + y2 = 1.625 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (y + 0.5) equal to 1.274754878 and -1.274754878.Subproblem 1
y + 0.5 = 1.274754878 Simplifying y + 0.5 = 1.274754878 Reorder the terms: 0.5 + y = 1.274754878 Solving 0.5 + y = 1.274754878 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 1.274754878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 1.274754878 + -0.5 y = 1.274754878 + -0.5 Combine like terms: 1.274754878 + -0.5 = 0.774754878 y = 0.774754878 Simplifying y = 0.774754878Subproblem 2
y + 0.5 = -1.274754878 Simplifying y + 0.5 = -1.274754878 Reorder the terms: 0.5 + y = -1.274754878 Solving 0.5 + y = -1.274754878 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -1.274754878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -1.274754878 + -0.5 y = -1.274754878 + -0.5 Combine like terms: -1.274754878 + -0.5 = -1.774754878 y = -1.774754878 Simplifying y = -1.774754878Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.774754878, -1.774754878}Solution
y = {0, 0.774754878, -1.774754878}
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