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Simplifying y2 + -20y = -29 Reorder the terms: -20y + y2 = -29 Solving -20y + y2 = -29 Solving for variable 'y'. Reorder the terms: 29 + -20y + y2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + -20y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -20y + -29 + y2 = 0 + -29 Reorder the terms: 29 + -29 + -20y + y2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -20y + y2 = 0 + -29 -20y + y2 = 0 + -29 Combine like terms: 0 + -29 = -29 -20y + y2 = -29 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 = -29 + 100 Reorder the terms: 100 + -20y + y2 = -29 + 100 Combine like terms: -29 + 100 = 71 100 + -20y + y2 = 71 Factor a perfect square on the left side: (y + -10)(y + -10) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (y + -10) equal to 8.426149773 and -8.426149773.Subproblem 1
y + -10 = 8.426149773 Simplifying y + -10 = 8.426149773 Reorder the terms: -10 + y = 8.426149773 Solving -10 + y = 8.426149773 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 = 8.426149773 + 10 Combine like terms: -10 + 10 = 0 0 + y = 8.426149773 + 10 y = 8.426149773 + 10 Combine like terms: 8.426149773 + 10 = 18.426149773 y = 18.426149773 Simplifying y = 18.426149773Subproblem 2
y + -10 = -8.426149773 Simplifying y + -10 = -8.426149773 Reorder the terms: -10 + y = -8.426149773 Solving -10 + y = -8.426149773 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 = -8.426149773 + 10 Combine like terms: -10 + 10 = 0 0 + y = -8.426149773 + 10 y = -8.426149773 + 10 Combine like terms: -8.426149773 + 10 = 1.573850227 y = 1.573850227 Simplifying y = 1.573850227Solution
The solution to the problem is based on the solutions from the subproblems. y = {18.426149773, 1.573850227}
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