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Simplifying 7y2 + -18y + 1 = 0 Reorder the terms: 1 + -18y + 7y2 = 0 Solving 1 + -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'. 0.1428571429 + -2.571428571y + y2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -2.571428571y + -0.1428571429 + y2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -2.571428571y + y2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -2.571428571y + y2 = 0 + -0.1428571429 -2.571428571y + y2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -2.571428571y + y2 = -0.1428571429 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 = -0.1428571429 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571y + y2 = -0.1428571429 + 1.653061225 Combine like terms: -0.1428571429 + 1.653061225 = 1.5102040821 1.653061225 + -2.571428571y + y2 = 1.5102040821 Factor a perfect square on the left side: (y + -1.285714286)(y + -1.285714286) = 1.5102040821 Calculate the square root of the right side: 1.22890361 Break this problem into two subproblems by setting (y + -1.285714286) equal to 1.22890361 and -1.22890361.Subproblem 1
y + -1.285714286 = 1.22890361 Simplifying y + -1.285714286 = 1.22890361 Reorder the terms: -1.285714286 + y = 1.22890361 Solving -1.285714286 + y = 1.22890361 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 = 1.22890361 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + y = 1.22890361 + 1.285714286 y = 1.22890361 + 1.285714286 Combine like terms: 1.22890361 + 1.285714286 = 2.514617896 y = 2.514617896 Simplifying y = 2.514617896Subproblem 2
y + -1.285714286 = -1.22890361 Simplifying y + -1.285714286 = -1.22890361 Reorder the terms: -1.285714286 + y = -1.22890361 Solving -1.285714286 + y = -1.22890361 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 = -1.22890361 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + y = -1.22890361 + 1.285714286 y = -1.22890361 + 1.285714286 Combine like terms: -1.22890361 + 1.285714286 = 0.056810676 y = 0.056810676 Simplifying y = 0.056810676Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.514617896, 0.056810676}
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