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Simplifying 30y3 + 84y + 120y2 = 0 Reorder the terms: 84y + 120y2 + 30y3 = 0 Solving 84y + 120y2 + 30y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '6y'. 6y(14 + 20y + 5y2) = 0 Ignore the factor 6.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 '(14 + 20y + 5y2)' equal to zero and attempt to solve: Simplifying 14 + 20y + 5y2 = 0 Solving 14 + 20y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + 4y + y2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 4y + -2.8 + y2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 4y + y2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 4y + y2 = 0 + -2.8 4y + y2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 4y + y2 = -2.8 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = -2.8 + 4 Reorder the terms: 4 + 4y + y2 = -2.8 + 4 Combine like terms: -2.8 + 4 = 1.2 4 + 4y + y2 = 1.2 Factor a perfect square on the left side: (y + 2)(y + 2) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (y + 2) equal to 1.095445115 and -1.095445115.Subproblem 1
y + 2 = 1.095445115 Simplifying y + 2 = 1.095445115 Reorder the terms: 2 + y = 1.095445115 Solving 2 + y = 1.095445115 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 1.095445115 + -2 Combine like terms: 2 + -2 = 0 0 + y = 1.095445115 + -2 y = 1.095445115 + -2 Combine like terms: 1.095445115 + -2 = -0.904554885 y = -0.904554885 Simplifying y = -0.904554885Subproblem 2
y + 2 = -1.095445115 Simplifying y + 2 = -1.095445115 Reorder the terms: 2 + y = -1.095445115 Solving 2 + y = -1.095445115 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -1.095445115 + -2 Combine like terms: 2 + -2 = 0 0 + y = -1.095445115 + -2 y = -1.095445115 + -2 Combine like terms: -1.095445115 + -2 = -3.095445115 y = -3.095445115 Simplifying y = -3.095445115Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.904554885, -3.095445115}Solution
y = {0, -0.904554885, -3.095445115}
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