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Simplifying (y + -5)(y + -5) = 20 Reorder the terms: (-5 + y)(y + -5) = 20 Reorder the terms: (-5 + y)(-5 + y) = 20 Multiply (-5 + y) * (-5 + y) (-5(-5 + y) + y(-5 + y)) = 20 ((-5 * -5 + y * -5) + y(-5 + y)) = 20 ((25 + -5y) + y(-5 + y)) = 20 (25 + -5y + (-5 * y + y * y)) = 20 (25 + -5y + (-5y + y2)) = 20 Combine like terms: -5y + -5y = -10y (25 + -10y + y2) = 20 Solving 25 + -10y + y2 = 20 Solving for variable 'y'. Reorder the terms: 25 + -20 + -10y + y2 = 20 + -20 Combine like terms: 25 + -20 = 5 5 + -10y + y2 = 20 + -20 Combine like terms: 20 + -20 = 0 5 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -10y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -10y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -10y + y2 = 0 + -5 -10y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -10y + y2 = -5 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 = -5 + 25 Reorder the terms: 25 + -10y + y2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + -10y + y2 = 20 Factor a perfect square on the left side: (y + -5)(y + -5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (y + -5) equal to 4.472135955 and -4.472135955.Subproblem 1
y + -5 = 4.472135955 Simplifying y + -5 = 4.472135955 Reorder the terms: -5 + y = 4.472135955 Solving -5 + y = 4.472135955 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 = 4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.472135955 + 5 y = 4.472135955 + 5 Combine like terms: 4.472135955 + 5 = 9.472135955 y = 9.472135955 Simplifying y = 9.472135955Subproblem 2
y + -5 = -4.472135955 Simplifying y + -5 = -4.472135955 Reorder the terms: -5 + y = -4.472135955 Solving -5 + y = -4.472135955 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 = -4.472135955 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.472135955 + 5 y = -4.472135955 + 5 Combine like terms: -4.472135955 + 5 = 0.527864045 y = 0.527864045 Simplifying y = 0.527864045Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.472135955, 0.527864045}
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