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Simplifying y2 + -2y + -104 = 0 Reorder the terms: -104 + -2y + y2 = 0 Solving -104 + -2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + -2y + 104 + y2 = 0 + 104 Reorder the terms: -104 + 104 + -2y + y2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + -2y + y2 = 0 + 104 -2y + y2 = 0 + 104 Combine like terms: 0 + 104 = 104 -2y + y2 = 104 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 104 + 1 Reorder the terms: 1 + -2y + y2 = 104 + 1 Combine like terms: 104 + 1 = 105 1 + -2y + y2 = 105 Factor a perfect square on the left side: (y + -1)(y + -1) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (y + -1) equal to 10.246950766 and -10.246950766.Subproblem 1
y + -1 = 10.246950766 Simplifying y + -1 = 10.246950766 Reorder the terms: -1 + y = 10.246950766 Solving -1 + y = 10.246950766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 10.246950766 + 1 Combine like terms: -1 + 1 = 0 0 + y = 10.246950766 + 1 y = 10.246950766 + 1 Combine like terms: 10.246950766 + 1 = 11.246950766 y = 11.246950766 Simplifying y = 11.246950766Subproblem 2
y + -1 = -10.246950766 Simplifying y + -1 = -10.246950766 Reorder the terms: -1 + y = -10.246950766 Solving -1 + y = -10.246950766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -10.246950766 + 1 Combine like terms: -1 + 1 = 0 0 + y = -10.246950766 + 1 y = -10.246950766 + 1 Combine like terms: -10.246950766 + 1 = -9.246950766 y = -9.246950766 Simplifying y = -9.246950766Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.246950766, -9.246950766}
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