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Simplifying y2 + -12y = 8 Reorder the terms: -12y + y2 = 8 Solving -12y + y2 = 8 Solving for variable 'y'. Reorder the terms: -8 + -12y + y2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -12y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + -12y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -12y + y2 = 0 + 8 -12y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 -12y + y2 = 8 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = 8 + 36 Reorder the terms: 36 + -12y + y2 = 8 + 36 Combine like terms: 8 + 36 = 44 36 + -12y + y2 = 44 Factor a perfect square on the left side: (y + -6)(y + -6) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (y + -6) equal to 6.633249581 and -6.633249581.Subproblem 1
y + -6 = 6.633249581 Simplifying y + -6 = 6.633249581 Reorder the terms: -6 + y = 6.633249581 Solving -6 + y = 6.633249581 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 6.633249581 + 6 Combine like terms: -6 + 6 = 0 0 + y = 6.633249581 + 6 y = 6.633249581 + 6 Combine like terms: 6.633249581 + 6 = 12.633249581 y = 12.633249581 Simplifying y = 12.633249581Subproblem 2
y + -6 = -6.633249581 Simplifying y + -6 = -6.633249581 Reorder the terms: -6 + y = -6.633249581 Solving -6 + y = -6.633249581 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -6.633249581 + 6 Combine like terms: -6 + 6 = 0 0 + y = -6.633249581 + 6 y = -6.633249581 + 6 Combine like terms: -6.633249581 + 6 = -0.633249581 y = -0.633249581 Simplifying y = -0.633249581Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.633249581, -0.633249581}
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