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Simplifying y2 + -1y + -164 = 0 Reorder the terms: -164 + -1y + y2 = 0 Solving -164 + -1y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + -1y + 164 + y2 = 0 + 164 Reorder the terms: -164 + 164 + -1y + y2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + -1y + y2 = 0 + 164 -1y + y2 = 0 + 164 Combine like terms: 0 + 164 = 164 -1y + y2 = 164 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 = 164 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 164 + 0.25 Combine like terms: 164 + 0.25 = 164.25 0.25 + -1y + y2 = 164.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 164.25 Calculate the square root of the right side: 12.816005618 Break this problem into two subproblems by setting (y + -0.5) equal to 12.816005618 and -12.816005618.Subproblem 1
y + -0.5 = 12.816005618 Simplifying y + -0.5 = 12.816005618 Reorder the terms: -0.5 + y = 12.816005618 Solving -0.5 + y = 12.816005618 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 = 12.816005618 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 12.816005618 + 0.5 y = 12.816005618 + 0.5 Combine like terms: 12.816005618 + 0.5 = 13.316005618 y = 13.316005618 Simplifying y = 13.316005618Subproblem 2
y + -0.5 = -12.816005618 Simplifying y + -0.5 = -12.816005618 Reorder the terms: -0.5 + y = -12.816005618 Solving -0.5 + y = -12.816005618 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 = -12.816005618 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -12.816005618 + 0.5 y = -12.816005618 + 0.5 Combine like terms: -12.816005618 + 0.5 = -12.316005618 y = -12.316005618 Simplifying y = -12.316005618Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.316005618, -12.316005618}
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