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Simplifying 6y2 + 2y + -5y3 = 0 Reorder the terms: 2y + 6y2 + -5y3 = 0 Solving 2y + 6y2 + -5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(2 + 6y + -5y2) = 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 '(2 + 6y + -5y2)' equal to zero and attempt to solve: Simplifying 2 + 6y + -5y2 = 0 Solving 2 + 6y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + -1.2y + y2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.2y + 0.4 + y2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.2y + y2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.2y + y2 = 0 + 0.4 -1.2y + y2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.2y + y2 = 0.4 The y term is -1.2y. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2y + 0.36 + y2 = 0.4 + 0.36 Reorder the terms: 0.36 + -1.2y + y2 = 0.4 + 0.36 Combine like terms: 0.4 + 0.36 = 0.76 0.36 + -1.2y + y2 = 0.76 Factor a perfect square on the left side: (y + -0.6)(y + -0.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (y + -0.6) equal to 0.871779789 and -0.871779789.Subproblem 1
y + -0.6 = 0.871779789 Simplifying y + -0.6 = 0.871779789 Reorder the terms: -0.6 + y = 0.871779789 Solving -0.6 + y = 0.871779789 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = 0.871779789 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = 0.871779789 + 0.6 y = 0.871779789 + 0.6 Combine like terms: 0.871779789 + 0.6 = 1.471779789 y = 1.471779789 Simplifying y = 1.471779789Subproblem 2
y + -0.6 = -0.871779789 Simplifying y + -0.6 = -0.871779789 Reorder the terms: -0.6 + y = -0.871779789 Solving -0.6 + y = -0.871779789 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = -0.871779789 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = -0.871779789 + 0.6 y = -0.871779789 + 0.6 Combine like terms: -0.871779789 + 0.6 = -0.271779789 y = -0.271779789 Simplifying y = -0.271779789Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.471779789, -0.271779789}Solution
y = {0, 1.471779789, -0.271779789}
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