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Simplifying y2 + -1y + -16 = 0 Reorder the terms: -16 + -1y + y2 = 0 Solving -16 + -1y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -1y + 16 + y2 = 0 + 16 Reorder the terms: -16 + 16 + -1y + y2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1y + y2 = 0 + 16 -1y + y2 = 0 + 16 Combine like terms: 0 + 16 = 16 -1y + y2 = 16 The y term is -1y. 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. -1y + 0.25 + y2 = 16 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 16 + 0.25 Combine like terms: 16 + 0.25 = 16.25 0.25 + -1y + y2 = 16.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (y + -0.5) equal to 4.031128874 and -4.031128874.Subproblem 1
y + -0.5 = 4.031128874 Simplifying y + -0.5 = 4.031128874 Reorder the terms: -0.5 + y = 4.031128874 Solving -0.5 + y = 4.031128874 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 = 4.031128874 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 4.031128874 + 0.5 y = 4.031128874 + 0.5 Combine like terms: 4.031128874 + 0.5 = 4.531128874 y = 4.531128874 Simplifying y = 4.531128874Subproblem 2
y + -0.5 = -4.031128874 Simplifying y + -0.5 = -4.031128874 Reorder the terms: -0.5 + y = -4.031128874 Solving -0.5 + y = -4.031128874 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 = -4.031128874 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -4.031128874 + 0.5 y = -4.031128874 + 0.5 Combine like terms: -4.031128874 + 0.5 = -3.531128874 y = -3.531128874 Simplifying y = -3.531128874Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.531128874, -3.531128874}
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