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Simplifying 5y3 + -1y2 + -2y = 0 Reorder the terms: -2y + -1y2 + 5y3 = 0 Solving -2y + -1y2 + 5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-2 + -1y + 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 '(-2 + -1y + 5y2)' equal to zero and attempt to solve: Simplifying -2 + -1y + 5y2 = 0 Solving -2 + -1y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -0.2y + y2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.2y + 0.4 + y2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.2y + y2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.2y + y2 = 0 + 0.4 -0.2y + y2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.2y + y2 = 0.4 The y term is -0.2y. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2y + 0.01 + y2 = 0.4 + 0.01 Reorder the terms: 0.01 + -0.2y + y2 = 0.4 + 0.01 Combine like terms: 0.4 + 0.01 = 0.41 0.01 + -0.2y + y2 = 0.41 Factor a perfect square on the left side: (y + -0.1)(y + -0.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (y + -0.1) equal to 0.640312424 and -0.640312424.Subproblem 1
y + -0.1 = 0.640312424 Simplifying y + -0.1 = 0.640312424 Reorder the terms: -0.1 + y = 0.640312424 Solving -0.1 + y = 0.640312424 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + y = 0.640312424 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + y = 0.640312424 + 0.1 y = 0.640312424 + 0.1 Combine like terms: 0.640312424 + 0.1 = 0.740312424 y = 0.740312424 Simplifying y = 0.740312424Subproblem 2
y + -0.1 = -0.640312424 Simplifying y + -0.1 = -0.640312424 Reorder the terms: -0.1 + y = -0.640312424 Solving -0.1 + y = -0.640312424 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + y = -0.640312424 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + y = -0.640312424 + 0.1 y = -0.640312424 + 0.1 Combine like terms: -0.640312424 + 0.1 = -0.540312424 y = -0.540312424 Simplifying y = -0.540312424Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.740312424, -0.540312424}Solution
y = {0, 0.740312424, -0.540312424}
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