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Simplifying y2 + 20y = -52 Reorder the terms: 20y + y2 = -52 Solving 20y + y2 = -52 Solving for variable 'y'. Reorder the terms: 52 + 20y + y2 = -52 + 52 Combine like terms: -52 + 52 = 0 52 + 20y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + 20y + -52 + y2 = 0 + -52 Reorder the terms: 52 + -52 + 20y + y2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + 20y + y2 = 0 + -52 20y + y2 = 0 + -52 Combine like terms: 0 + -52 = -52 20y + y2 = -52 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 = -52 + 100 Reorder the terms: 100 + 20y + y2 = -52 + 100 Combine like terms: -52 + 100 = 48 100 + 20y + y2 = 48 Factor a perfect square on the left side: (y + 10)(y + 10) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (y + 10) equal to 6.92820323 and -6.92820323.Subproblem 1
y + 10 = 6.92820323 Simplifying y + 10 = 6.92820323 Reorder the terms: 10 + y = 6.92820323 Solving 10 + y = 6.92820323 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 = 6.92820323 + -10 Combine like terms: 10 + -10 = 0 0 + y = 6.92820323 + -10 y = 6.92820323 + -10 Combine like terms: 6.92820323 + -10 = -3.07179677 y = -3.07179677 Simplifying y = -3.07179677Subproblem 2
y + 10 = -6.92820323 Simplifying y + 10 = -6.92820323 Reorder the terms: 10 + y = -6.92820323 Solving 10 + y = -6.92820323 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 = -6.92820323 + -10 Combine like terms: 10 + -10 = 0 0 + y = -6.92820323 + -10 y = -6.92820323 + -10 Combine like terms: -6.92820323 + -10 = -16.92820323 y = -16.92820323 Simplifying y = -16.92820323Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.07179677, -16.92820323}
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