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Simplifying y2 + 2y = 140 Reorder the terms: 2y + y2 = 140 Solving 2y + y2 = 140 Solving for variable 'y'. Reorder the terms: -140 + 2y + y2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + 2y + 140 + y2 = 0 + 140 Reorder the terms: -140 + 140 + 2y + y2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 2y + y2 = 0 + 140 2y + y2 = 0 + 140 Combine like terms: 0 + 140 = 140 2y + y2 = 140 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 = 140 + 1 Reorder the terms: 1 + 2y + y2 = 140 + 1 Combine like terms: 140 + 1 = 141 1 + 2y + y2 = 141 Factor a perfect square on the left side: (y + 1)(y + 1) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (y + 1) equal to 11.874342087 and -11.874342087.Subproblem 1
y + 1 = 11.874342087 Simplifying y + 1 = 11.874342087 Reorder the terms: 1 + y = 11.874342087 Solving 1 + y = 11.874342087 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 = 11.874342087 + -1 Combine like terms: 1 + -1 = 0 0 + y = 11.874342087 + -1 y = 11.874342087 + -1 Combine like terms: 11.874342087 + -1 = 10.874342087 y = 10.874342087 Simplifying y = 10.874342087Subproblem 2
y + 1 = -11.874342087 Simplifying y + 1 = -11.874342087 Reorder the terms: 1 + y = -11.874342087 Solving 1 + y = -11.874342087 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 = -11.874342087 + -1 Combine like terms: 1 + -1 = 0 0 + y = -11.874342087 + -1 y = -11.874342087 + -1 Combine like terms: -11.874342087 + -1 = -12.874342087 y = -12.874342087 Simplifying y = -12.874342087Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.874342087, -12.874342087}
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