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Simplifying (28y2) + -4y = 1 Reorder the terms: -4y + (28y2) = 1 Solving -4y + (28y2) = 1 Solving for variable 'y'. Reorder the terms: -1 + -4y + (28y2) = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -4y + (28y2) = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.03571428571 + -0.1428571429y + y2 = 0 Move the constant term to the right: Add '0.03571428571' to each side of the equation. -0.03571428571 + -0.1428571429y + 0.03571428571 + y2 = 0 + 0.03571428571 Reorder the terms: -0.03571428571 + 0.03571428571 + -0.1428571429y + y2 = 0 + 0.03571428571 Combine like terms: -0.03571428571 + 0.03571428571 = 0.00000000000 0.00000000000 + -0.1428571429y + y2 = 0 + 0.03571428571 -0.1428571429y + y2 = 0 + 0.03571428571 Combine like terms: 0 + 0.03571428571 = 0.03571428571 -0.1428571429y + y2 = 0.03571428571 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 = 0.03571428571 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429y + y2 = 0.03571428571 + 0.005102040819 Combine like terms: 0.03571428571 + 0.005102040819 = 0.040816326529 0.005102040819 + -0.1428571429y + y2 = 0.040816326529 Factor a perfect square on the left side: ((y) + -0.07142857145)((y) + -0.07142857145) = 0.040816326529 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting ((y) + -0.07142857145) equal to 0.202030509 and -0.202030509.Subproblem 1
(y) + -0.07142857145 = 0.202030509 Simplifying (y) + -0.07142857145 = 0.202030509 y + -0.07142857145 = 0.202030509 Reorder the terms: -0.07142857145 + y = 0.202030509 Solving -0.07142857145 + y = 0.202030509 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 = 0.202030509 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + y = 0.202030509 + 0.07142857145 y = 0.202030509 + 0.07142857145 Combine like terms: 0.202030509 + 0.07142857145 = 0.27345908045 y = 0.27345908045 Simplifying y = 0.27345908045Subproblem 2
(y) + -0.07142857145 = -0.202030509 Simplifying (y) + -0.07142857145 = -0.202030509 y + -0.07142857145 = -0.202030509 Reorder the terms: -0.07142857145 + y = -0.202030509 Solving -0.07142857145 + y = -0.202030509 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 = -0.202030509 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + y = -0.202030509 + 0.07142857145 y = -0.202030509 + 0.07142857145 Combine like terms: -0.202030509 + 0.07142857145 = -0.13060193755 y = -0.13060193755 Simplifying y = -0.13060193755Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.27345908045, -0.13060193755}
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