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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 = 155 100 + -20y + y2 = 155 Factor a perfect square on the left side: (y + -10)(y + -10) = 155 Calculate the square root of the right side: 12.449899598 Break this problem into two subproblems by setting (y + -10) equal to 12.449899598 and -12.449899598.Subproblem 1
y + -10 = 12.449899598 Simplifying y + -10 = 12.449899598 Reorder the terms: -10 + y = 12.449899598 Solving -10 + y = 12.449899598 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 = 12.449899598 + 10 Combine like terms: -10 + 10 = 0 0 + y = 12.449899598 + 10 y = 12.449899598 + 10 Combine like terms: 12.449899598 + 10 = 22.449899598 y = 22.449899598 Simplifying y = 22.449899598Subproblem 2
y + -10 = -12.449899598 Simplifying y + -10 = -12.449899598 Reorder the terms: -10 + y = -12.449899598 Solving -10 + y = -12.449899598 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 = -12.449899598 + 10 Combine like terms: -10 + 10 = 0 0 + y = -12.449899598 + 10 y = -12.449899598 + 10 Combine like terms: -12.449899598 + 10 = -2.449899598 y = -2.449899598 Simplifying y = -2.449899598Solution
The solution to the problem is based on the solutions from the subproblems. y = {22.449899598, -2.449899598}
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