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Simplifying 141y + -1y2 + -260 = 0 Reorder the terms: -260 + 141y + -1y2 = 0 Solving -260 + 141y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 260 + -141y + y2 = 0 Move the constant term to the right: Add '-260' to each side of the equation. 260 + -141y + -260 + y2 = 0 + -260 Reorder the terms: 260 + -260 + -141y + y2 = 0 + -260 Combine like terms: 260 + -260 = 0 0 + -141y + y2 = 0 + -260 -141y + y2 = 0 + -260 Combine like terms: 0 + -260 = -260 -141y + y2 = -260 The y term is -141y. Take half its coefficient (-70.5). Square it (4970.25) and add it to both sides. Add '4970.25' to each side of the equation. -141y + 4970.25 + y2 = -260 + 4970.25 Reorder the terms: 4970.25 + -141y + y2 = -260 + 4970.25 Combine like terms: -260 + 4970.25 = 4710.25 4970.25 + -141y + y2 = 4710.25 Factor a perfect square on the left side: (y + -70.5)(y + -70.5) = 4710.25 Calculate the square root of the right side: 68.631261099 Break this problem into two subproblems by setting (y + -70.5) equal to 68.631261099 and -68.631261099.Subproblem 1
y + -70.5 = 68.631261099 Simplifying y + -70.5 = 68.631261099 Reorder the terms: -70.5 + y = 68.631261099 Solving -70.5 + y = 68.631261099 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '70.5' to each side of the equation. -70.5 + 70.5 + y = 68.631261099 + 70.5 Combine like terms: -70.5 + 70.5 = 0.0 0.0 + y = 68.631261099 + 70.5 y = 68.631261099 + 70.5 Combine like terms: 68.631261099 + 70.5 = 139.131261099 y = 139.131261099 Simplifying y = 139.131261099Subproblem 2
y + -70.5 = -68.631261099 Simplifying y + -70.5 = -68.631261099 Reorder the terms: -70.5 + y = -68.631261099 Solving -70.5 + y = -68.631261099 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '70.5' to each side of the equation. -70.5 + 70.5 + y = -68.631261099 + 70.5 Combine like terms: -70.5 + 70.5 = 0.0 0.0 + y = -68.631261099 + 70.5 y = -68.631261099 + 70.5 Combine like terms: -68.631261099 + 70.5 = 1.868738901 y = 1.868738901 Simplifying y = 1.868738901Solution
The solution to the problem is based on the solutions from the subproblems. y = {139.131261099, 1.868738901}
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