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Simplifying (-2y2 + -8y) + (3y2 + 2y + -8) = 0 Reorder the terms: (-8y + -2y2) + (3y2 + 2y + -8) = 0 Remove parenthesis around (-8y + -2y2) -8y + -2y2 + (3y2 + 2y + -8) = 0 Reorder the terms: -8y + -2y2 + (-8 + 2y + 3y2) = 0 Remove parenthesis around (-8 + 2y + 3y2) -8y + -2y2 + -8 + 2y + 3y2 = 0 Reorder the terms: -8 + -8y + 2y + -2y2 + 3y2 = 0 Combine like terms: -8y + 2y = -6y -8 + -6y + -2y2 + 3y2 = 0 Combine like terms: -2y2 + 3y2 = 1y2 -8 + -6y + 1y2 = 0 Solving -8 + -6y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. 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 = 7.123105626 y = 7.123105626 Simplifying y = 7.123105626Subproblem 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 = -1.123105626 y = -1.123105626 Simplifying y = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.123105626, -1.123105626}
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