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Simplifying 7y2 + 18y + -8 = 0 Reorder the terms: -8 + 18y + 7y2 = 0 Solving -8 + 18y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 2.571428571y + y2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 2.571428571y + 1.142857143 + y2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 2.571428571y + y2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 2.571428571y + y2 = 0 + 1.142857143 2.571428571y + y2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 2.571428571y + y2 = 1.142857143 The y term is 2.571428571y. Take half its coefficient (1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. 2.571428571y + 1.653061225 + y2 = 1.142857143 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571y + y2 = 1.142857143 + 1.653061225 Combine like terms: 1.142857143 + 1.653061225 = 2.795918368 1.653061225 + 2.571428571y + y2 = 2.795918368 Factor a perfect square on the left side: (y + 1.285714286)(y + 1.285714286) = 2.795918368 Calculate the square root of the right side: 1.672099987 Break this problem into two subproblems by setting (y + 1.285714286) equal to 1.672099987 and -1.672099987.Subproblem 1
y + 1.285714286 = 1.672099987 Simplifying y + 1.285714286 = 1.672099987 Reorder the terms: 1.285714286 + y = 1.672099987 Solving 1.285714286 + y = 1.672099987 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + y = 1.672099987 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + y = 1.672099987 + -1.285714286 y = 1.672099987 + -1.285714286 Combine like terms: 1.672099987 + -1.285714286 = 0.386385701 y = 0.386385701 Simplifying y = 0.386385701Subproblem 2
y + 1.285714286 = -1.672099987 Simplifying y + 1.285714286 = -1.672099987 Reorder the terms: 1.285714286 + y = -1.672099987 Solving 1.285714286 + y = -1.672099987 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + y = -1.672099987 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + y = -1.672099987 + -1.285714286 y = -1.672099987 + -1.285714286 Combine like terms: -1.672099987 + -1.285714286 = -2.957814273 y = -2.957814273 Simplifying y = -2.957814273Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.386385701, -2.957814273}
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