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Simplifying y2 + -10y + -116 = 0 Reorder the terms: -116 + -10y + y2 = 0 Solving -116 + -10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + -10y + 116 + y2 = 0 + 116 Reorder the terms: -116 + 116 + -10y + y2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + -10y + y2 = 0 + 116 -10y + y2 = 0 + 116 Combine like terms: 0 + 116 = 116 -10y + y2 = 116 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 116 + 25 Reorder the terms: 25 + -10y + y2 = 116 + 25 Combine like terms: 116 + 25 = 141 25 + -10y + y2 = 141 Factor a perfect square on the left side: (y + -5)(y + -5) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (y + -5) equal to 11.874342087 and -11.874342087.Subproblem 1
y + -5 = 11.874342087 Simplifying y + -5 = 11.874342087 Reorder the terms: -5 + y = 11.874342087 Solving -5 + y = 11.874342087 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 11.874342087 + 5 Combine like terms: -5 + 5 = 0 0 + y = 11.874342087 + 5 y = 11.874342087 + 5 Combine like terms: 11.874342087 + 5 = 16.874342087 y = 16.874342087 Simplifying y = 16.874342087Subproblem 2
y + -5 = -11.874342087 Simplifying y + -5 = -11.874342087 Reorder the terms: -5 + y = -11.874342087 Solving -5 + y = -11.874342087 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -11.874342087 + 5 Combine like terms: -5 + 5 = 0 0 + y = -11.874342087 + 5 y = -11.874342087 + 5 Combine like terms: -11.874342087 + 5 = -6.874342087 y = -6.874342087 Simplifying y = -6.874342087Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.874342087, -6.874342087}
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