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Simplifying y2 + 20y + 80 = 0 Reorder the terms: 80 + 20y + y2 = 0 Solving 80 + 20y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 20y + -80 + y2 = 0 + -80 Reorder the terms: 80 + -80 + 20y + y2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 20y + y2 = 0 + -80 20y + y2 = 0 + -80 Combine like terms: 0 + -80 = -80 20y + y2 = -80 The y term is 20y. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20y + 100 + y2 = -80 + 100 Reorder the terms: 100 + 20y + y2 = -80 + 100 Combine like terms: -80 + 100 = 20 100 + 20y + y2 = 20 Factor a perfect square on the left side: (y + 10)(y + 10) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (y + 10) equal to 4.472135955 and -4.472135955.Subproblem 1
y + 10 = 4.472135955 Simplifying y + 10 = 4.472135955 Reorder the terms: 10 + y = 4.472135955 Solving 10 + y = 4.472135955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + y = 4.472135955 + -10 Combine like terms: 10 + -10 = 0 0 + y = 4.472135955 + -10 y = 4.472135955 + -10 Combine like terms: 4.472135955 + -10 = -5.527864045 y = -5.527864045 Simplifying y = -5.527864045Subproblem 2
y + 10 = -4.472135955 Simplifying y + 10 = -4.472135955 Reorder the terms: 10 + y = -4.472135955 Solving 10 + y = -4.472135955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + y = -4.472135955 + -10 Combine like terms: 10 + -10 = 0 0 + y = -4.472135955 + -10 y = -4.472135955 + -10 Combine like terms: -4.472135955 + -10 = -14.472135955 y = -14.472135955 Simplifying y = -14.472135955Solution
The solution to the problem is based on the solutions from the subproblems. y = {-5.527864045, -14.472135955}
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