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Simplifying y2 + -10y = -4y + -2 Reorder the terms: -10y + y2 = -4y + -2 Reorder the terms: -10y + y2 = -2 + -4y Solving -10y + y2 = -2 + -4y Solving for variable 'y'. Reorder the terms: 2 + -10y + 4y + y2 = -2 + -4y + 2 + 4y Combine like terms: -10y + 4y = -6y 2 + -6y + y2 = -2 + -4y + 2 + 4y Reorder the terms: 2 + -6y + y2 = -2 + 2 + -4y + 4y Combine like terms: -2 + 2 = 0 2 + -6y + y2 = 0 + -4y + 4y 2 + -6y + y2 = -4y + 4y Combine like terms: -4y + 4y = 0 2 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -6y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6y + y2 = 0 + -2 -6y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6y + y2 = -2 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 = -2 + 9 Reorder the terms: 9 + -6y + y2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6y + y2 = 7 Factor a perfect square on the left side: (y + -3)(y + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
y + -3 = 2.645751311 Simplifying y + -3 = 2.645751311 Reorder the terms: -3 + y = 2.645751311 Solving -3 + y = 2.645751311 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 = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + y = 2.645751311 + 3 y = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 y = 5.645751311 Simplifying y = 5.645751311Subproblem 2
y + -3 = -2.645751311 Simplifying y + -3 = -2.645751311 Reorder the terms: -3 + y = -2.645751311 Solving -3 + y = -2.645751311 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 = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + y = -2.645751311 + 3 y = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 y = 0.354248689 Simplifying y = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.645751311, 0.354248689}
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