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Simplifying y2 = 10y + -18 Reorder the terms: y2 = -18 + 10y Solving y2 = -18 + 10y Solving for variable 'y'. Reorder the terms: 18 + -10y + y2 = -18 + 10y + 18 + -10y Reorder the terms: 18 + -10y + y2 = -18 + 18 + 10y + -10y Combine like terms: -18 + 18 = 0 18 + -10y + y2 = 0 + 10y + -10y 18 + -10y + y2 = 10y + -10y Combine like terms: 10y + -10y = 0 18 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -10y + -18 + y2 = 0 + -18 Reorder the terms: 18 + -18 + -10y + y2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -10y + y2 = 0 + -18 -10y + y2 = 0 + -18 Combine like terms: 0 + -18 = -18 -10y + y2 = -18 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = -18 + 25 Reorder the terms: 25 + -10y + y2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + -10y + y2 = 7 Factor a perfect square on the left side: (y + -5)(y + -5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + -5) equal to 2.645751311 and -2.645751311.Subproblem 1
y + -5 = 2.645751311 Simplifying y + -5 = 2.645751311 Reorder the terms: -5 + y = 2.645751311 Solving -5 + y = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + y = 2.645751311 + 5 y = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 y = 7.645751311 Simplifying y = 7.645751311Subproblem 2
y + -5 = -2.645751311 Simplifying y + -5 = -2.645751311 Reorder the terms: -5 + y = -2.645751311 Solving -5 + y = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + y = -2.645751311 + 5 y = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 y = 2.354248689 Simplifying y = 2.354248689Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.645751311, 2.354248689}
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