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Simplifying 5y3 + -34y2 + -5y = 0 Reorder the terms: -5y + -34y2 + 5y3 = 0 Solving -5y + -34y2 + 5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-5 + -34y + 5y2) = 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 '(-5 + -34y + 5y2)' equal to zero and attempt to solve: Simplifying -5 + -34y + 5y2 = 0 Solving -5 + -34y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -6.8y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.8y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -6.8y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.8y + y2 = 0 + 1 -6.8y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.8y + y2 = 1 The y term is -6.8y. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8y + 11.56 + y2 = 1 + 11.56 Reorder the terms: 11.56 + -6.8y + y2 = 1 + 11.56 Combine like terms: 1 + 11.56 = 12.56 11.56 + -6.8y + y2 = 12.56 Factor a perfect square on the left side: (y + -3.4)(y + -3.4) = 12.56 Calculate the square root of the right side: 3.544009029 Break this problem into two subproblems by setting (y + -3.4) equal to 3.544009029 and -3.544009029.Subproblem 1
y + -3.4 = 3.544009029 Simplifying y + -3.4 = 3.544009029 Reorder the terms: -3.4 + y = 3.544009029 Solving -3.4 + y = 3.544009029 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + y = 3.544009029 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + y = 3.544009029 + 3.4 y = 3.544009029 + 3.4 Combine like terms: 3.544009029 + 3.4 = 6.944009029 y = 6.944009029 Simplifying y = 6.944009029Subproblem 2
y + -3.4 = -3.544009029 Simplifying y + -3.4 = -3.544009029 Reorder the terms: -3.4 + y = -3.544009029 Solving -3.4 + y = -3.544009029 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + y = -3.544009029 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + y = -3.544009029 + 3.4 y = -3.544009029 + 3.4 Combine like terms: -3.544009029 + 3.4 = -0.144009029 y = -0.144009029 Simplifying y = -0.144009029Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.944009029, -0.144009029}Solution
y = {0, 6.944009029, -0.144009029}
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