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Simplifying y2 + -189y + 8810 = 0 Reorder the terms: 8810 + -189y + y2 = 0 Solving 8810 + -189y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-8810' to each side of the equation. 8810 + -189y + -8810 + y2 = 0 + -8810 Reorder the terms: 8810 + -8810 + -189y + y2 = 0 + -8810 Combine like terms: 8810 + -8810 = 0 0 + -189y + y2 = 0 + -8810 -189y + y2 = 0 + -8810 Combine like terms: 0 + -8810 = -8810 -189y + y2 = -8810 The y term is -189y. Take half its coefficient (-94.5). Square it (8930.25) and add it to both sides. Add '8930.25' to each side of the equation. -189y + 8930.25 + y2 = -8810 + 8930.25 Reorder the terms: 8930.25 + -189y + y2 = -8810 + 8930.25 Combine like terms: -8810 + 8930.25 = 120.25 8930.25 + -189y + y2 = 120.25 Factor a perfect square on the left side: (y + -94.5)(y + -94.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (y + -94.5) equal to 10.9658561 and -10.9658561.Subproblem 1
y + -94.5 = 10.9658561 Simplifying y + -94.5 = 10.9658561 Reorder the terms: -94.5 + y = 10.9658561 Solving -94.5 + y = 10.9658561 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '94.5' to each side of the equation. -94.5 + 94.5 + y = 10.9658561 + 94.5 Combine like terms: -94.5 + 94.5 = 0.0 0.0 + y = 10.9658561 + 94.5 y = 10.9658561 + 94.5 Combine like terms: 10.9658561 + 94.5 = 105.4658561 y = 105.4658561 Simplifying y = 105.4658561Subproblem 2
y + -94.5 = -10.9658561 Simplifying y + -94.5 = -10.9658561 Reorder the terms: -94.5 + y = -10.9658561 Solving -94.5 + y = -10.9658561 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '94.5' to each side of the equation. -94.5 + 94.5 + y = -10.9658561 + 94.5 Combine like terms: -94.5 + 94.5 = 0.0 0.0 + y = -10.9658561 + 94.5 y = -10.9658561 + 94.5 Combine like terms: -10.9658561 + 94.5 = 83.5341439 y = 83.5341439 Simplifying y = 83.5341439Solution
The solution to the problem is based on the solutions from the subproblems. y = {105.4658561, 83.5341439}
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