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Simplifying y2 + -8y + -16 = -7y + 88 Reorder the terms: -16 + -8y + y2 = -7y + 88 Reorder the terms: -16 + -8y + y2 = 88 + -7y Solving -16 + -8y + y2 = 88 + -7y Solving for variable 'y'. Reorder the terms: -16 + -88 + -8y + 7y + y2 = 88 + -7y + -88 + 7y Combine like terms: -16 + -88 = -104 -104 + -8y + 7y + y2 = 88 + -7y + -88 + 7y Combine like terms: -8y + 7y = -1y -104 + -1y + y2 = 88 + -7y + -88 + 7y Reorder the terms: -104 + -1y + y2 = 88 + -88 + -7y + 7y Combine like terms: 88 + -88 = 0 -104 + -1y + y2 = 0 + -7y + 7y -104 + -1y + y2 = -7y + 7y Combine like terms: -7y + 7y = 0 -104 + -1y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + -1y + 104 + y2 = 0 + 104 Reorder the terms: -104 + 104 + -1y + y2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + -1y + y2 = 0 + 104 -1y + y2 = 0 + 104 Combine like terms: 0 + 104 = 104 -1y + y2 = 104 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 = 104 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 104 + 0.25 Combine like terms: 104 + 0.25 = 104.25 0.25 + -1y + y2 = 104.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (y + -0.5) equal to 10.210288928 and -10.210288928.Subproblem 1
y + -0.5 = 10.210288928 Simplifying y + -0.5 = 10.210288928 Reorder the terms: -0.5 + y = 10.210288928 Solving -0.5 + y = 10.210288928 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 = 10.210288928 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 10.210288928 + 0.5 y = 10.210288928 + 0.5 Combine like terms: 10.210288928 + 0.5 = 10.710288928 y = 10.710288928 Simplifying y = 10.710288928Subproblem 2
y + -0.5 = -10.210288928 Simplifying y + -0.5 = -10.210288928 Reorder the terms: -0.5 + y = -10.210288928 Solving -0.5 + y = -10.210288928 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 = -10.210288928 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -10.210288928 + 0.5 y = -10.210288928 + 0.5 Combine like terms: -10.210288928 + 0.5 = -9.710288928 y = -9.710288928 Simplifying y = -9.710288928Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.710288928, -9.710288928}
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