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Simplifying 10y3 + 20y2 + -6y = 0 Reorder the terms: -6y + 20y2 + 10y3 = 0 Solving -6y + 20y2 + 10y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(-3 + 10y + 5y2) = 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 '(-3 + 10y + 5y2)' equal to zero and attempt to solve: Simplifying -3 + 10y + 5y2 = 0 Solving -3 + 10y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 2y + y2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 2y + 0.6 + y2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 2y + y2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 2y + y2 = 0 + 0.6 2y + y2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 2y + y2 = 0.6 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 0.6 + 1 Reorder the terms: 1 + 2y + y2 = 0.6 + 1 Combine like terms: 0.6 + 1 = 1.6 1 + 2y + y2 = 1.6 Factor a perfect square on the left side: (y + 1)(y + 1) = 1.6 Calculate the square root of the right side: 1.264911064 Break this problem into two subproblems by setting (y + 1) equal to 1.264911064 and -1.264911064.Subproblem 1
y + 1 = 1.264911064 Simplifying y + 1 = 1.264911064 Reorder the terms: 1 + y = 1.264911064 Solving 1 + y = 1.264911064 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 1.264911064 + -1 Combine like terms: 1 + -1 = 0 0 + y = 1.264911064 + -1 y = 1.264911064 + -1 Combine like terms: 1.264911064 + -1 = 0.264911064 y = 0.264911064 Simplifying y = 0.264911064Subproblem 2
y + 1 = -1.264911064 Simplifying y + 1 = -1.264911064 Reorder the terms: 1 + y = -1.264911064 Solving 1 + y = -1.264911064 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -1.264911064 + -1 Combine like terms: 1 + -1 = 0 0 + y = -1.264911064 + -1 y = -1.264911064 + -1 Combine like terms: -1.264911064 + -1 = -2.264911064 y = -2.264911064 Simplifying y = -2.264911064Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.264911064, -2.264911064}Solution
y = {0, 0.264911064, -2.264911064}
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