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Simplifying y2 + -6y + 64 = 10y + 14 Reorder the terms: 64 + -6y + y2 = 10y + 14 Reorder the terms: 64 + -6y + y2 = 14 + 10y Solving 64 + -6y + y2 = 14 + 10y Solving for variable 'y'. Reorder the terms: 64 + -14 + -6y + -10y + y2 = 14 + 10y + -14 + -10y Combine like terms: 64 + -14 = 50 50 + -6y + -10y + y2 = 14 + 10y + -14 + -10y Combine like terms: -6y + -10y = -16y 50 + -16y + y2 = 14 + 10y + -14 + -10y Reorder the terms: 50 + -16y + y2 = 14 + -14 + 10y + -10y Combine like terms: 14 + -14 = 0 50 + -16y + y2 = 0 + 10y + -10y 50 + -16y + y2 = 10y + -10y Combine like terms: 10y + -10y = 0 50 + -16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -16y + -50 + y2 = 0 + -50 Reorder the terms: 50 + -50 + -16y + y2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -16y + y2 = 0 + -50 -16y + y2 = 0 + -50 Combine like terms: 0 + -50 = -50 -16y + y2 = -50 The y term is -16y. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16y + 64 + y2 = -50 + 64 Reorder the terms: 64 + -16y + y2 = -50 + 64 Combine like terms: -50 + 64 = 14 64 + -16y + y2 = 14 Factor a perfect square on the left side: (y + -8)(y + -8) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (y + -8) equal to 3.741657387 and -3.741657387.Subproblem 1
y + -8 = 3.741657387 Simplifying y + -8 = 3.741657387 Reorder the terms: -8 + y = 3.741657387 Solving -8 + y = 3.741657387 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = 3.741657387 + 8 Combine like terms: -8 + 8 = 0 0 + y = 3.741657387 + 8 y = 3.741657387 + 8 Combine like terms: 3.741657387 + 8 = 11.741657387 y = 11.741657387 Simplifying y = 11.741657387Subproblem 2
y + -8 = -3.741657387 Simplifying y + -8 = -3.741657387 Reorder the terms: -8 + y = -3.741657387 Solving -8 + y = -3.741657387 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = -3.741657387 + 8 Combine like terms: -8 + 8 = 0 0 + y = -3.741657387 + 8 y = -3.741657387 + 8 Combine like terms: -3.741657387 + 8 = 4.258342613 y = 4.258342613 Simplifying y = 4.258342613Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.741657387, 4.258342613}
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