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Simplifying -1y(y2 + -7) + 4y2(2y + -6) = 0 Reorder the terms: -1y(-7 + y2) + 4y2(2y + -6) = 0 (-7 * -1y + y2 * -1y) + 4y2(2y + -6) = 0 (7y + -1y3) + 4y2(2y + -6) = 0 Reorder the terms: 7y + -1y3 + 4y2(-6 + 2y) = 0 7y + -1y3 + (-6 * 4y2 + 2y * 4y2) = 0 7y + -1y3 + (-24y2 + 8y3) = 0 Reorder the terms: 7y + -24y2 + -1y3 + 8y3 = 0 Combine like terms: -1y3 + 8y3 = 7y3 7y + -24y2 + 7y3 = 0 Solving 7y + -24y2 + 7y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(7 + -24y + 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 '(7 + -24y + 7y2)' equal to zero and attempt to solve: Simplifying 7 + -24y + 7y2 = 0 Solving 7 + -24y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + -3.428571429y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.428571429y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -3.428571429y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.428571429y + y2 = 0 + -1 -3.428571429y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.428571429y + y2 = -1 The y term is -3.428571429y. Take half its coefficient (-1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. -3.428571429y + 2.938775513 + y2 = -1 + 2.938775513 Reorder the terms: 2.938775513 + -3.428571429y + y2 = -1 + 2.938775513 Combine like terms: -1 + 2.938775513 = 1.938775513 2.938775513 + -3.428571429y + y2 = 1.938775513 Factor a perfect square on the left side: (y + -1.714285715)(y + -1.714285715) = 1.938775513 Calculate the square root of the right side: 1.392399193 Break this problem into two subproblems by setting (y + -1.714285715) equal to 1.392399193 and -1.392399193.Subproblem 1
y + -1.714285715 = 1.392399193 Simplifying y + -1.714285715 = 1.392399193 Reorder the terms: -1.714285715 + y = 1.392399193 Solving -1.714285715 + y = 1.392399193 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + y = 1.392399193 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + y = 1.392399193 + 1.714285715 y = 1.392399193 + 1.714285715 Combine like terms: 1.392399193 + 1.714285715 = 3.106684908 y = 3.106684908 Simplifying y = 3.106684908Subproblem 2
y + -1.714285715 = -1.392399193 Simplifying y + -1.714285715 = -1.392399193 Reorder the terms: -1.714285715 + y = -1.392399193 Solving -1.714285715 + y = -1.392399193 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + y = -1.392399193 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + y = -1.392399193 + 1.714285715 y = -1.392399193 + 1.714285715 Combine like terms: -1.392399193 + 1.714285715 = 0.321886522 y = 0.321886522 Simplifying y = 0.321886522Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.106684908, 0.321886522}Solution
y = {0, 3.106684908, 0.321886522}
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