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Simplifying 16y2 + 32y + -49 = 0 Reorder the terms: -49 + 32y + 16y2 = 0 Solving -49 + 32y + 16y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.0625 + 2y + y2 = 0 Move the constant term to the right: Add '3.0625' to each side of the equation. -3.0625 + 2y + 3.0625 + y2 = 0 + 3.0625 Reorder the terms: -3.0625 + 3.0625 + 2y + y2 = 0 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + 2y + y2 = 0 + 3.0625 2y + y2 = 0 + 3.0625 Combine like terms: 0 + 3.0625 = 3.0625 2y + y2 = 3.0625 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 3.0625 + 1 Reorder the terms: 1 + 2y + y2 = 3.0625 + 1 Combine like terms: 3.0625 + 1 = 4.0625 1 + 2y + y2 = 4.0625 Factor a perfect square on the left side: (y + 1)(y + 1) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (y + 1) equal to 2.015564437 and -2.015564437.Subproblem 1
y + 1 = 2.015564437 Simplifying y + 1 = 2.015564437 Reorder the terms: 1 + y = 2.015564437 Solving 1 + y = 2.015564437 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 2.015564437 + -1 Combine like terms: 1 + -1 = 0 0 + y = 2.015564437 + -1 y = 2.015564437 + -1 Combine like terms: 2.015564437 + -1 = 1.015564437 y = 1.015564437 Simplifying y = 1.015564437Subproblem 2
y + 1 = -2.015564437 Simplifying y + 1 = -2.015564437 Reorder the terms: 1 + y = -2.015564437 Solving 1 + y = -2.015564437 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -2.015564437 + -1 Combine like terms: 1 + -1 = 0 0 + y = -2.015564437 + -1 y = -2.015564437 + -1 Combine like terms: -2.015564437 + -1 = -3.015564437 y = -3.015564437 Simplifying y = -3.015564437Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.015564437, -3.015564437}
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