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Simplifying 2y2 + -4y + -8 = y2 + y Reorder the terms: -8 + -4y + 2y2 = y2 + y Reorder the terms: -8 + -4y + 2y2 = y + y2 Solving -8 + -4y + 2y2 = y + y2 Solving for variable 'y'. Reorder the terms: -8 + -4y + -1y + 2y2 + -1y2 = y + y2 + -1y + -1y2 Combine like terms: -4y + -1y = -5y -8 + -5y + 2y2 + -1y2 = y + y2 + -1y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -8 + -5y + 1y2 = y + y2 + -1y + -1y2 Reorder the terms: -8 + -5y + 1y2 = y + -1y + y2 + -1y2 Combine like terms: y + -1y = 0 -8 + -5y + 1y2 = 0 + y2 + -1y2 -8 + -5y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -8 + -5y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -5y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + -5y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5y + y2 = 0 + 8 -5y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 -5y + y2 = 8 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = 8 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 8 + 6.25 Combine like terms: 8 + 6.25 = 14.25 6.25 + -5y + y2 = 14.25 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (y + -2.5) equal to 3.774917218 and -3.774917218.Subproblem 1
y + -2.5 = 3.774917218 Simplifying y + -2.5 = 3.774917218 Reorder the terms: -2.5 + y = 3.774917218 Solving -2.5 + y = 3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 3.774917218 + 2.5 y = 3.774917218 + 2.5 Combine like terms: 3.774917218 + 2.5 = 6.274917218 y = 6.274917218 Simplifying y = 6.274917218Subproblem 2
y + -2.5 = -3.774917218 Simplifying y + -2.5 = -3.774917218 Reorder the terms: -2.5 + y = -3.774917218 Solving -2.5 + y = -3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -3.774917218 + 2.5 y = -3.774917218 + 2.5 Combine like terms: -3.774917218 + 2.5 = -1.274917218 y = -1.274917218 Simplifying y = -1.274917218Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.274917218, -1.274917218}
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