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Simplifying 8y + -6y2 + -1y3 = 0 Solving 8y + -6y2 + -1y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(8 + -6y + -1y2) = 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 '(8 + -6y + -1y2)' equal to zero and attempt to solve: Simplifying 8 + -6y + -1y2 = 0 Solving 8 + -6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 6y + y2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 6y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + 6y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6y + y2 = 0 + 8 6y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 6y + y2 = 8 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 = 8 + 9 Reorder the terms: 9 + 6y + y2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + 6y + y2 = 17 Factor a perfect square on the left side: (y + 3)(y + 3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (y + 3) equal to 4.123105626 and -4.123105626.Subproblem 1
y + 3 = 4.123105626 Simplifying y + 3 = 4.123105626 Reorder the terms: 3 + y = 4.123105626 Solving 3 + y = 4.123105626 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 = 4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + y = 4.123105626 + -3 y = 4.123105626 + -3 Combine like terms: 4.123105626 + -3 = 1.123105626 y = 1.123105626 Simplifying y = 1.123105626Subproblem 2
y + 3 = -4.123105626 Simplifying y + 3 = -4.123105626 Reorder the terms: 3 + y = -4.123105626 Solving 3 + y = -4.123105626 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 = -4.123105626 + -3 Combine like terms: 3 + -3 = 0 0 + y = -4.123105626 + -3 y = -4.123105626 + -3 Combine like terms: -4.123105626 + -3 = -7.123105626 y = -7.123105626 Simplifying y = -7.123105626Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.123105626, -7.123105626}Solution
y = {0, 1.123105626, -7.123105626}
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