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Simplifying 16y2 + 16y + -3 = 0 Reorder the terms: -3 + 16y + 16y2 = 0 Solving -3 + 16y + 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'. -0.1875 + y + y2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + y + 0.1875 + y2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + y + y2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + y + y2 = 0 + 0.1875 y + y2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 y + y2 = 0.1875 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + y2 = 0.1875 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = 0.1875 + 0.25 Combine like terms: 0.1875 + 0.25 = 0.4375 1.25 + y2 = 0.4375 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (y + 0.5) equal to 0.661437828 and -0.661437828.Subproblem 1
y + 0.5 = 0.661437828 Simplifying y + 0.5 = 0.661437828 Reorder the terms: 0.5 + y = 0.661437828 Solving 0.5 + y = 0.661437828 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 0.661437828 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 0.661437828 + -0.5 y = 0.661437828 + -0.5 Combine like terms: 0.661437828 + -0.5 = 0.161437828 y = 0.161437828 Simplifying y = 0.161437828Subproblem 2
y + 0.5 = -0.661437828 Simplifying y + 0.5 = -0.661437828 Reorder the terms: 0.5 + y = -0.661437828 Solving 0.5 + y = -0.661437828 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -0.661437828 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -0.661437828 + -0.5 y = -0.661437828 + -0.5 Combine like terms: -0.661437828 + -0.5 = -1.161437828 y = -1.161437828 Simplifying y = -1.161437828Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.161437828, -1.161437828}
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