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Simplifying 4y3 + 24y2 + 2y = 0 Reorder the terms: 2y + 24y2 + 4y3 = 0 Solving 2y + 24y2 + 4y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(1 + 12y + 2y2) = 0 Ignore the factor 2.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 '(1 + 12y + 2y2)' equal to zero and attempt to solve: Simplifying 1 + 12y + 2y2 = 0 Solving 1 + 12y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 6y + y2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 6y + -0.5 + y2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 6y + y2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 6y + y2 = 0 + -0.5 6y + y2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 6y + y2 = -0.5 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -0.5 + 9 Reorder the terms: 9 + 6y + y2 = -0.5 + 9 Combine like terms: -0.5 + 9 = 8.5 9 + 6y + y2 = 8.5 Factor a perfect square on the left side: (y + 3)(y + 3) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (y + 3) equal to 2.915475947 and -2.915475947.Subproblem 1
y + 3 = 2.915475947 Simplifying y + 3 = 2.915475947 Reorder the terms: 3 + y = 2.915475947 Solving 3 + y = 2.915475947 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 2.915475947 + -3 Combine like terms: 3 + -3 = 0 0 + y = 2.915475947 + -3 y = 2.915475947 + -3 Combine like terms: 2.915475947 + -3 = -0.084524053 y = -0.084524053 Simplifying y = -0.084524053Subproblem 2
y + 3 = -2.915475947 Simplifying y + 3 = -2.915475947 Reorder the terms: 3 + y = -2.915475947 Solving 3 + y = -2.915475947 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -2.915475947 + -3 Combine like terms: 3 + -3 = 0 0 + y = -2.915475947 + -3 y = -2.915475947 + -3 Combine like terms: -2.915475947 + -3 = -5.915475947 y = -5.915475947 Simplifying y = -5.915475947Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.084524053, -5.915475947}Solution
y = {0, -0.084524053, -5.915475947}
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