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Simplifying a4 + -6a2 + -1 = 0 Reorder the terms: -1 + -6a2 + a4 = 0 Solving -1 + -6a2 + a4 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -6a2 + 1 + a4 = 0 + 1 Reorder the terms: -1 + 1 + -6a2 + a4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6a2 + a4 = 0 + 1 -6a2 + a4 = 0 + 1 Combine like terms: 0 + 1 = 1 -6a2 + a4 = 1 The a term is -6a2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a2 + 9 + a4 = 1 + 9 Reorder the terms: 9 + -6a2 + a4 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6a2 + a4 = 10 Factor a perfect square on the left side: (a2 + -3)(a2 + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (a2 + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
a2 + -3 = 3.16227766 Simplifying a2 + -3 = 3.16227766 Reorder the terms: -3 + a2 = 3.16227766 Solving -3 + a2 = 3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a2 = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + a2 = 3.16227766 + 3 a2 = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 a2 = 6.16227766 Simplifying a2 = 6.16227766 Take the square root of each side: a = {-2.482393534, 2.482393534}Subproblem 2
a2 + -3 = -3.16227766 Simplifying a2 + -3 = -3.16227766 Reorder the terms: -3 + a2 = -3.16227766 Solving -3 + a2 = -3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a2 = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + a2 = -3.16227766 + 3 a2 = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 a2 = -0.16227766 Simplifying a2 = -0.16227766 Reorder the terms: 0.16227766 + a2 = -0.16227766 + 0.16227766 Combine like terms: -0.16227766 + 0.16227766 = 0.00000000 0.16227766 + a2 = 0.00000000 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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