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Simplifying 2y + -6y2 + 3 + -1y2 = 0 Reorder the terms: 3 + 2y + -6y2 + -1y2 = 0 Combine like terms: -6y2 + -1y2 = -7y2 3 + 2y + -7y2 = 0 Solving 3 + 2y + -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'. -0.4285714286 + -0.2857142857y + y2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.2857142857y + 0.4285714286 + y2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.2857142857y + y2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.2857142857y + y2 = 0 + 0.4285714286 -0.2857142857y + y2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.2857142857y + y2 = 0.4285714286 The y term is -0.2857142857y. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857y + 0.02040816328 + y2 = 0.4285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857y + y2 = 0.4285714286 + 0.02040816328 Combine like terms: 0.4285714286 + 0.02040816328 = 0.44897959188 0.02040816328 + -0.2857142857y + y2 = 0.44897959188 Factor a perfect square on the left side: (y + -0.1428571429)(y + -0.1428571429) = 0.44897959188 Calculate the square root of the right side: 0.670059394 Break this problem into two subproblems by setting (y + -0.1428571429) equal to 0.670059394 and -0.670059394.Subproblem 1
y + -0.1428571429 = 0.670059394 Simplifying y + -0.1428571429 = 0.670059394 Reorder the terms: -0.1428571429 + y = 0.670059394 Solving -0.1428571429 + y = 0.670059394 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + y = 0.670059394 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + y = 0.670059394 + 0.1428571429 y = 0.670059394 + 0.1428571429 Combine like terms: 0.670059394 + 0.1428571429 = 0.8129165369 y = 0.8129165369 Simplifying y = 0.8129165369Subproblem 2
y + -0.1428571429 = -0.670059394 Simplifying y + -0.1428571429 = -0.670059394 Reorder the terms: -0.1428571429 + y = -0.670059394 Solving -0.1428571429 + y = -0.670059394 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + y = -0.670059394 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + y = -0.670059394 + 0.1428571429 y = -0.670059394 + 0.1428571429 Combine like terms: -0.670059394 + 0.1428571429 = -0.5272022511 y = -0.5272022511 Simplifying y = -0.5272022511Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.8129165369, -0.5272022511}
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