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Simplifying 7y2 + -10 + 11 = y + 17 Reorder the terms: -10 + 11 + 7y2 = y + 17 Combine like terms: -10 + 11 = 1 1 + 7y2 = y + 17 Reorder the terms: 1 + 7y2 = 17 + y Solving 1 + 7y2 = 17 + y Solving for variable 'y'. Reorder the terms: 1 + -17 + -1y + 7y2 = 17 + y + -17 + -1y Combine like terms: 1 + -17 = -16 -16 + -1y + 7y2 = 17 + y + -17 + -1y Reorder the terms: -16 + -1y + 7y2 = 17 + -17 + y + -1y Combine like terms: 17 + -17 = 0 -16 + -1y + 7y2 = 0 + y + -1y -16 + -1y + 7y2 = y + -1y Combine like terms: y + -1y = 0 -16 + -1y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + -0.1428571429y + y2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -0.1428571429y + 2.285714286 + y2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -0.1428571429y + y2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -0.1428571429y + y2 = 0 + 2.285714286 -0.1428571429y + y2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -0.1428571429y + y2 = 2.285714286 The y term is -0.1428571429y. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429y + 0.005102040819 + y2 = 2.285714286 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429y + y2 = 2.285714286 + 0.005102040819 Combine like terms: 2.285714286 + 0.005102040819 = 2.290816326819 0.005102040819 + -0.1428571429y + y2 = 2.290816326819 Factor a perfect square on the left side: (y + -0.07142857145)(y + -0.07142857145) = 2.290816326819 Calculate the square root of the right side: 1.513544293 Break this problem into two subproblems by setting (y + -0.07142857145) equal to 1.513544293 and -1.513544293.Subproblem 1
y + -0.07142857145 = 1.513544293 Simplifying y + -0.07142857145 = 1.513544293 Reorder the terms: -0.07142857145 + y = 1.513544293 Solving -0.07142857145 + y = 1.513544293 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + y = 1.513544293 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + y = 1.513544293 + 0.07142857145 y = 1.513544293 + 0.07142857145 Combine like terms: 1.513544293 + 0.07142857145 = 1.58497286445 y = 1.58497286445 Simplifying y = 1.58497286445Subproblem 2
y + -0.07142857145 = -1.513544293 Simplifying y + -0.07142857145 = -1.513544293 Reorder the terms: -0.07142857145 + y = -1.513544293 Solving -0.07142857145 + y = -1.513544293 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + y = -1.513544293 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + y = -1.513544293 + 0.07142857145 y = -1.513544293 + 0.07142857145 Combine like terms: -1.513544293 + 0.07142857145 = -1.44211572155 y = -1.44211572155 Simplifying y = -1.44211572155Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.58497286445, -1.44211572155}
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