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Simplifying a8 + a4 + 1 = 32 Reorder the terms: 1 + a4 + a8 = 32 Solving 1 + a4 + a8 = 32 Solving for variable 'a'. Reorder the terms: 1 + -32 + a4 + a8 = 32 + -32 Combine like terms: 1 + -32 = -31 -31 + a4 + a8 = 32 + -32 Combine like terms: 32 + -32 = 0 -31 + a4 + a8 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + a4 + 31 + a8 = 0 + 31 Reorder the terms: -31 + 31 + a4 + a8 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + a4 + a8 = 0 + 31 a4 + a8 = 0 + 31 Combine like terms: 0 + 31 = 31 a4 + a8 = 31 The a term is a4. 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. a4 + 0.25 + a8 = 31 + 0.25 Reorder the terms: 0.25 + a4 + a8 = 31 + 0.25 Combine like terms: 31 + 0.25 = 31.25 0.25 + a4 + a8 = 31.25 Factor a perfect square on the left side: (a4 + 0.5)(a4 + 0.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (a4 + 0.5) equal to 5.590169944 and -5.590169944.Subproblem 1
a4 + 0.5 = 5.590169944 Simplifying a4 + 0.5 = 5.590169944 Reorder the terms: 0.5 + a4 = 5.590169944 Solving 0.5 + a4 = 5.590169944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a4 = 5.590169944 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a4 = 5.590169944 + -0.5 a4 = 5.590169944 + -0.5 Combine like terms: 5.590169944 + -0.5 = 5.090169944 a4 = 5.090169944 Simplifying a4 = 5.090169944 Reorder the terms: -5.090169944 + a4 = 5.090169944 + -5.090169944 Combine like terms: 5.090169944 + -5.090169944 = 0.000000000 -5.090169944 + a4 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
a4 + 0.5 = -5.590169944 Simplifying a4 + 0.5 = -5.590169944 Reorder the terms: 0.5 + a4 = -5.590169944 Solving 0.5 + a4 = -5.590169944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a4 = -5.590169944 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a4 = -5.590169944 + -0.5 a4 = -5.590169944 + -0.5 Combine like terms: -5.590169944 + -0.5 = -6.090169944 a4 = -6.090169944 Simplifying a4 = -6.090169944 Reorder the terms: 6.090169944 + a4 = -6.090169944 + 6.090169944 Combine like terms: -6.090169944 + 6.090169944 = 0.000000000 6.090169944 + a4 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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