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Simplifying y2 + -20y + 55 = 0 Reorder the terms: 55 + -20y + y2 = 0 Solving 55 + -20y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + -20y + -55 + y2 = 0 + -55 Reorder the terms: 55 + -55 + -20y + y2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -20y + y2 = 0 + -55 -20y + y2 = 0 + -55 Combine like terms: 0 + -55 = -55 -20y + y2 = -55 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 = -55 + 100 Reorder the terms: 100 + -20y + y2 = -55 + 100 Combine like terms: -55 + 100 = 45 100 + -20y + y2 = 45 Factor a perfect square on the left side: (y + -10)(y + -10) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (y + -10) equal to 6.708203933 and -6.708203933.Subproblem 1
y + -10 = 6.708203933 Simplifying y + -10 = 6.708203933 Reorder the terms: -10 + y = 6.708203933 Solving -10 + y = 6.708203933 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 = 6.708203933 + 10 Combine like terms: -10 + 10 = 0 0 + y = 6.708203933 + 10 y = 6.708203933 + 10 Combine like terms: 6.708203933 + 10 = 16.708203933 y = 16.708203933 Simplifying y = 16.708203933Subproblem 2
y + -10 = -6.708203933 Simplifying y + -10 = -6.708203933 Reorder the terms: -10 + y = -6.708203933 Solving -10 + y = -6.708203933 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 = -6.708203933 + 10 Combine like terms: -10 + 10 = 0 0 + y = -6.708203933 + 10 y = -6.708203933 + 10 Combine like terms: -6.708203933 + 10 = 3.291796067 y = 3.291796067 Simplifying y = 3.291796067Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.708203933, 3.291796067}
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