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Simplifying (3y2 + 2y + -6) + -1(2y2 + -1y + 2) = 0 Reorder the terms: (-6 + 2y + 3y2) + -1(2y2 + -1y + 2) = 0 Remove parenthesis around (-6 + 2y + 3y2) -6 + 2y + 3y2 + -1(2y2 + -1y + 2) = 0 Reorder the terms: -6 + 2y + 3y2 + -1(2 + -1y + 2y2) = 0 -6 + 2y + 3y2 + (2 * -1 + -1y * -1 + 2y2 * -1) = 0 -6 + 2y + 3y2 + (-2 + 1y + -2y2) = 0 Reorder the terms: -6 + -2 + 2y + 1y + 3y2 + -2y2 = 0 Combine like terms: -6 + -2 = -8 -8 + 2y + 1y + 3y2 + -2y2 = 0 Combine like terms: 2y + 1y = 3y -8 + 3y + 3y2 + -2y2 = 0 Combine like terms: 3y2 + -2y2 = 1y2 -8 + 3y + 1y2 = 0 Solving -8 + 3y + 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 + 3y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + 3y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3y + y2 = 0 + 8 3y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 3y + y2 = 8 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = 8 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + 3y + y2 = 10.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (y + 1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
y + 1.5 = 3.201562119 Simplifying y + 1.5 = 3.201562119 Reorder the terms: 1.5 + y = 3.201562119 Solving 1.5 + y = 3.201562119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 3.201562119 + -1.5 y = 3.201562119 + -1.5 Combine like terms: 3.201562119 + -1.5 = 1.701562119 y = 1.701562119 Simplifying y = 1.701562119Subproblem 2
y + 1.5 = -3.201562119 Simplifying y + 1.5 = -3.201562119 Reorder the terms: 1.5 + y = -3.201562119 Solving 1.5 + y = -3.201562119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -3.201562119 + -1.5 y = -3.201562119 + -1.5 Combine like terms: -3.201562119 + -1.5 = -4.701562119 y = -4.701562119 Simplifying y = -4.701562119Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.701562119, -4.701562119}
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