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Simplifying y2 + -8y + -117 = 0 Reorder the terms: -117 + -8y + y2 = 0 Solving -117 + -8y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + -8y + 117 + y2 = 0 + 117 Reorder the terms: -117 + 117 + -8y + y2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + -8y + y2 = 0 + 117 -8y + y2 = 0 + 117 Combine like terms: 0 + 117 = 117 -8y + y2 = 117 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 117 + 16 Reorder the terms: 16 + -8y + y2 = 117 + 16 Combine like terms: 117 + 16 = 133 16 + -8y + y2 = 133 Factor a perfect square on the left side: (y + -4)(y + -4) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (y + -4) equal to 11.532562595 and -11.532562595.Subproblem 1
y + -4 = 11.532562595 Simplifying y + -4 = 11.532562595 Reorder the terms: -4 + y = 11.532562595 Solving -4 + y = 11.532562595 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 11.532562595 + 4 Combine like terms: -4 + 4 = 0 0 + y = 11.532562595 + 4 y = 11.532562595 + 4 Combine like terms: 11.532562595 + 4 = 15.532562595 y = 15.532562595 Simplifying y = 15.532562595Subproblem 2
y + -4 = -11.532562595 Simplifying y + -4 = -11.532562595 Reorder the terms: -4 + y = -11.532562595 Solving -4 + y = -11.532562595 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -11.532562595 + 4 Combine like terms: -4 + 4 = 0 0 + y = -11.532562595 + 4 y = -11.532562595 + 4 Combine like terms: -11.532562595 + 4 = -7.532562595 y = -7.532562595 Simplifying y = -7.532562595Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.532562595, -7.532562595}
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