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Simplifying -3y3 + -6y2 = 2y Reorder the terms: -6y2 + -3y3 = 2y Solving -6y2 + -3y3 = 2y Solving for variable 'y'. Reorder the terms: -2y + -6y2 + -3y3 = 2y + -2y Combine like terms: 2y + -2y = 0 -2y + -6y2 + -3y3 = 0 Factor out the Greatest Common Factor (GCF), '-1y'. -1y(2 + 6y + 3y2) = 0 Ignore the factor -1.Subproblem 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 + 6y + 3y2)' equal to zero and attempt to solve: Simplifying 2 + 6y + 3y2 = 0 Solving 2 + 6y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 2y + y2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 2y + -0.6666666667 + y2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 2y + y2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 2y + y2 = 0 + -0.6666666667 2y + y2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 2y + y2 = -0.6666666667 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = -0.6666666667 + 1 Reorder the terms: 1 + 2y + y2 = -0.6666666667 + 1 Combine like terms: -0.6666666667 + 1 = 0.3333333333 1 + 2y + y2 = 0.3333333333 Factor a perfect square on the left side: (y + 1)(y + 1) = 0.3333333333 Calculate the square root of the right side: 0.577350269 Break this problem into two subproblems by setting (y + 1) equal to 0.577350269 and -0.577350269.Subproblem 1
y + 1 = 0.577350269 Simplifying y + 1 = 0.577350269 Reorder the terms: 1 + y = 0.577350269 Solving 1 + y = 0.577350269 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 0.577350269 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0.577350269 + -1 y = 0.577350269 + -1 Combine like terms: 0.577350269 + -1 = -0.422649731 y = -0.422649731 Simplifying y = -0.422649731Subproblem 2
y + 1 = -0.577350269 Simplifying y + 1 = -0.577350269 Reorder the terms: 1 + y = -0.577350269 Solving 1 + y = -0.577350269 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -0.577350269 + -1 Combine like terms: 1 + -1 = 0 0 + y = -0.577350269 + -1 y = -0.577350269 + -1 Combine like terms: -0.577350269 + -1 = -1.577350269 y = -1.577350269 Simplifying y = -1.577350269Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.422649731, -1.577350269}Solution
y = {0, -0.422649731, -1.577350269}
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