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Simplifying 7y3 + -21y2 + -11y = 0 Reorder the terms: -11y + -21y2 + 7y3 = 0 Solving -11y + -21y2 + 7y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-11 + -21y + 7y2) = 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 + -21y + 7y2)' equal to zero and attempt to solve: Simplifying -11 + -21y + 7y2 = 0 Solving -11 + -21y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.571428571 + -3y + y2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + -3y + 1.571428571 + y2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + -3y + y2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + -3y + y2 = 0 + 1.571428571 -3y + y2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 -3y + y2 = 1.571428571 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 1.571428571 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 1.571428571 + 2.25 Combine like terms: 1.571428571 + 2.25 = 3.821428571 2.25 + -3y + y2 = 3.821428571 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 3.821428571 Calculate the square root of the right side: 1.954847455 Break this problem into two subproblems by setting (y + -1.5) equal to 1.954847455 and -1.954847455.Subproblem 1
y + -1.5 = 1.954847455 Simplifying y + -1.5 = 1.954847455 Reorder the terms: -1.5 + y = 1.954847455 Solving -1.5 + y = 1.954847455 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 1.954847455 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 1.954847455 + 1.5 y = 1.954847455 + 1.5 Combine like terms: 1.954847455 + 1.5 = 3.454847455 y = 3.454847455 Simplifying y = 3.454847455Subproblem 2
y + -1.5 = -1.954847455 Simplifying y + -1.5 = -1.954847455 Reorder the terms: -1.5 + y = -1.954847455 Solving -1.5 + y = -1.954847455 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -1.954847455 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -1.954847455 + 1.5 y = -1.954847455 + 1.5 Combine like terms: -1.954847455 + 1.5 = -0.454847455 y = -0.454847455 Simplifying y = -0.454847455Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.454847455, -0.454847455}Solution
y = {0, 3.454847455, -0.454847455}
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