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Simplifying y2 + -1y + -140 = 0 Reorder the terms: -140 + -1y + y2 = 0 Solving -140 + -1y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -1y + 140 + y2 = 0 + 140 Reorder the terms: -140 + 140 + -1y + y2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -1y + y2 = 0 + 140 -1y + y2 = 0 + 140 Combine like terms: 0 + 140 = 140 -1y + y2 = 140 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 140 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 140 + 0.25 Combine like terms: 140 + 0.25 = 140.25 0.25 + -1y + y2 = 140.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (y + -0.5) equal to 11.842719282 and -11.842719282.Subproblem 1
y + -0.5 = 11.842719282 Simplifying y + -0.5 = 11.842719282 Reorder the terms: -0.5 + y = 11.842719282 Solving -0.5 + y = 11.842719282 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 11.842719282 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 11.842719282 + 0.5 y = 11.842719282 + 0.5 Combine like terms: 11.842719282 + 0.5 = 12.342719282 y = 12.342719282 Simplifying y = 12.342719282Subproblem 2
y + -0.5 = -11.842719282 Simplifying y + -0.5 = -11.842719282 Reorder the terms: -0.5 + y = -11.842719282 Solving -0.5 + y = -11.842719282 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -11.842719282 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -11.842719282 + 0.5 y = -11.842719282 + 0.5 Combine like terms: -11.842719282 + 0.5 = -11.342719282 y = -11.342719282 Simplifying y = -11.342719282Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.342719282, -11.342719282}
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