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Simplifying (66 + y)(55 + y) + -57.333 = 33 Multiply (66 + y) * (55 + y) (66(55 + y) + y(55 + y)) + -57.333 = 33 ((55 * 66 + y * 66) + y(55 + y)) + -57.333 = 33 ((3630 + 66y) + y(55 + y)) + -57.333 = 33 (3630 + 66y + (55 * y + y * y)) + -57.333 = 33 (3630 + 66y + (55y + y2)) + -57.333 = 33 Combine like terms: 66y + 55y = 121y (3630 + 121y + y2) + -57.333 = 33 Reorder the terms: 3630 + -57.333 + 121y + y2 = 33 Combine like terms: 3630 + -57.333 = 3572.667 3572.667 + 121y + y2 = 33 Solving 3572.667 + 121y + y2 = 33 Solving for variable 'y'. Reorder the terms: 3572.667 + -33 + 121y + y2 = 33 + -33 Combine like terms: 3572.667 + -33 = 3539.667 3539.667 + 121y + y2 = 33 + -33 Combine like terms: 33 + -33 = 0 3539.667 + 121y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3539.667' to each side of the equation. 3539.667 + 121y + -3539.667 + y2 = 0 + -3539.667 Reorder the terms: 3539.667 + -3539.667 + 121y + y2 = 0 + -3539.667 Combine like terms: 3539.667 + -3539.667 = 0.000 0.000 + 121y + y2 = 0 + -3539.667 121y + y2 = 0 + -3539.667 Combine like terms: 0 + -3539.667 = -3539.667 121y + y2 = -3539.667 The y term is 121y. Take half its coefficient (60.5). Square it (3660.25) and add it to both sides. Add '3660.25' to each side of the equation. 121y + 3660.25 + y2 = -3539.667 + 3660.25 Reorder the terms: 3660.25 + 121y + y2 = -3539.667 + 3660.25 Combine like terms: -3539.667 + 3660.25 = 120.583 3660.25 + 121y + y2 = 120.583 Factor a perfect square on the left side: (y + 60.5)(y + 60.5) = 120.583 Calculate the square root of the right side: 10.981029096 Break this problem into two subproblems by setting (y + 60.5) equal to 10.981029096 and -10.981029096.Subproblem 1
y + 60.5 = 10.981029096 Simplifying y + 60.5 = 10.981029096 Reorder the terms: 60.5 + y = 10.981029096 Solving 60.5 + y = 10.981029096 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-60.5' to each side of the equation. 60.5 + -60.5 + y = 10.981029096 + -60.5 Combine like terms: 60.5 + -60.5 = 0.0 0.0 + y = 10.981029096 + -60.5 y = 10.981029096 + -60.5 Combine like terms: 10.981029096 + -60.5 = -49.518970904 y = -49.518970904 Simplifying y = -49.518970904Subproblem 2
y + 60.5 = -10.981029096 Simplifying y + 60.5 = -10.981029096 Reorder the terms: 60.5 + y = -10.981029096 Solving 60.5 + y = -10.981029096 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-60.5' to each side of the equation. 60.5 + -60.5 + y = -10.981029096 + -60.5 Combine like terms: 60.5 + -60.5 = 0.0 0.0 + y = -10.981029096 + -60.5 y = -10.981029096 + -60.5 Combine like terms: -10.981029096 + -60.5 = -71.481029096 y = -71.481029096 Simplifying y = -71.481029096Solution
The solution to the problem is based on the solutions from the subproblems. y = {-49.518970904, -71.481029096}
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