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Simplifying y2 + 20y + -200 = 0 Reorder the terms: -200 + 20y + y2 = 0 Solving -200 + 20y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 20y + 200 + y2 = 0 + 200 Reorder the terms: -200 + 200 + 20y + y2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 20y + y2 = 0 + 200 20y + y2 = 0 + 200 Combine like terms: 0 + 200 = 200 20y + y2 = 200 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 = 200 + 100 Reorder the terms: 100 + 20y + y2 = 200 + 100 Combine like terms: 200 + 100 = 300 100 + 20y + y2 = 300 Factor a perfect square on the left side: (y + 10)(y + 10) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (y + 10) equal to 17.320508076 and -17.320508076.Subproblem 1
y + 10 = 17.320508076 Simplifying y + 10 = 17.320508076 Reorder the terms: 10 + y = 17.320508076 Solving 10 + y = 17.320508076 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 = 17.320508076 + -10 Combine like terms: 10 + -10 = 0 0 + y = 17.320508076 + -10 y = 17.320508076 + -10 Combine like terms: 17.320508076 + -10 = 7.320508076 y = 7.320508076 Simplifying y = 7.320508076Subproblem 2
y + 10 = -17.320508076 Simplifying y + 10 = -17.320508076 Reorder the terms: 10 + y = -17.320508076 Solving 10 + y = -17.320508076 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 = -17.320508076 + -10 Combine like terms: 10 + -10 = 0 0 + y = -17.320508076 + -10 y = -17.320508076 + -10 Combine like terms: -17.320508076 + -10 = -27.320508076 y = -27.320508076 Simplifying y = -27.320508076Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.320508076, -27.320508076}
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