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Simplifying 3y3 + -15y2 + -440y = 0 Reorder the terms: -440y + -15y2 + 3y3 = 0 Solving -440y + -15y2 + 3y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-440 + -15y + 3y2) = 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 '(-440 + -15y + 3y2)' equal to zero and attempt to solve: Simplifying -440 + -15y + 3y2 = 0 Solving -440 + -15y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -146.6666667 + -5y + y2 = 0 Move the constant term to the right: Add '146.6666667' to each side of the equation. -146.6666667 + -5y + 146.6666667 + y2 = 0 + 146.6666667 Reorder the terms: -146.6666667 + 146.6666667 + -5y + y2 = 0 + 146.6666667 Combine like terms: -146.6666667 + 146.6666667 = 0.0000000 0.0000000 + -5y + y2 = 0 + 146.6666667 -5y + y2 = 0 + 146.6666667 Combine like terms: 0 + 146.6666667 = 146.6666667 -5y + y2 = 146.6666667 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = 146.6666667 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 146.6666667 + 6.25 Combine like terms: 146.6666667 + 6.25 = 152.9166667 6.25 + -5y + y2 = 152.9166667 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 152.9166667 Calculate the square root of the right side: 12.365947869 Break this problem into two subproblems by setting (y + -2.5) equal to 12.365947869 and -12.365947869.Subproblem 1
y + -2.5 = 12.365947869 Simplifying y + -2.5 = 12.365947869 Reorder the terms: -2.5 + y = 12.365947869 Solving -2.5 + y = 12.365947869 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 12.365947869 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 12.365947869 + 2.5 y = 12.365947869 + 2.5 Combine like terms: 12.365947869 + 2.5 = 14.865947869 y = 14.865947869 Simplifying y = 14.865947869Subproblem 2
y + -2.5 = -12.365947869 Simplifying y + -2.5 = -12.365947869 Reorder the terms: -2.5 + y = -12.365947869 Solving -2.5 + y = -12.365947869 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -12.365947869 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -12.365947869 + 2.5 y = -12.365947869 + 2.5 Combine like terms: -12.365947869 + 2.5 = -9.865947869 y = -9.865947869 Simplifying y = -9.865947869Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.865947869, -9.865947869}Solution
y = {0, 14.865947869, -9.865947869}
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