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Simplifying 16y2 + -3y + -16 = 0 Reorder the terms: -16 + -3y + 16y2 = 0 Solving -16 + -3y + 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'. -1 + -0.1875y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.1875y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -0.1875y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.1875y + y2 = 0 + 1 -0.1875y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.1875y + y2 = 1 The y term is -0.1875y. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875y + 0.0087890625 + y2 = 1 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875y + y2 = 1 + 0.0087890625 Combine like terms: 1 + 0.0087890625 = 1.0087890625 0.0087890625 + -0.1875y + y2 = 1.0087890625 Factor a perfect square on the left side: (y + -0.09375)(y + -0.09375) = 1.0087890625 Calculate the square root of the right side: 1.004384918 Break this problem into two subproblems by setting (y + -0.09375) equal to 1.004384918 and -1.004384918.Subproblem 1
y + -0.09375 = 1.004384918 Simplifying y + -0.09375 = 1.004384918 Reorder the terms: -0.09375 + y = 1.004384918 Solving -0.09375 + y = 1.004384918 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + y = 1.004384918 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + y = 1.004384918 + 0.09375 y = 1.004384918 + 0.09375 Combine like terms: 1.004384918 + 0.09375 = 1.098134918 y = 1.098134918 Simplifying y = 1.098134918Subproblem 2
y + -0.09375 = -1.004384918 Simplifying y + -0.09375 = -1.004384918 Reorder the terms: -0.09375 + y = -1.004384918 Solving -0.09375 + y = -1.004384918 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + y = -1.004384918 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + y = -1.004384918 + 0.09375 y = -1.004384918 + 0.09375 Combine like terms: -1.004384918 + 0.09375 = -0.910634918 y = -0.910634918 Simplifying y = -0.910634918Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.098134918, -0.910634918}
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