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Simplifying a4 + -4a2 + -6 = 0 Reorder the terms: -6 + -4a2 + a4 = 0 Solving -6 + -4a2 + a4 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -4a2 + 6 + a4 = 0 + 6 Reorder the terms: -6 + 6 + -4a2 + a4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4a2 + a4 = 0 + 6 -4a2 + a4 = 0 + 6 Combine like terms: 0 + 6 = 6 -4a2 + a4 = 6 The a term is -4a2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a2 + 4 + a4 = 6 + 4 Reorder the terms: 4 + -4a2 + a4 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + -4a2 + a4 = 10 Factor a perfect square on the left side: (a2 + -2)(a2 + -2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (a2 + -2) equal to 3.16227766 and -3.16227766.Subproblem 1
a2 + -2 = 3.16227766 Simplifying a2 + -2 = 3.16227766 Reorder the terms: -2 + a2 = 3.16227766 Solving -2 + a2 = 3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a2 = 3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + a2 = 3.16227766 + 2 a2 = 3.16227766 + 2 Combine like terms: 3.16227766 + 2 = 5.16227766 a2 = 5.16227766 Simplifying a2 = 5.16227766 Take the square root of each side: a = {-2.272064625, 2.272064625}Subproblem 2
a2 + -2 = -3.16227766 Simplifying a2 + -2 = -3.16227766 Reorder the terms: -2 + a2 = -3.16227766 Solving -2 + a2 = -3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a2 = -3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + a2 = -3.16227766 + 2 a2 = -3.16227766 + 2 Combine like terms: -3.16227766 + 2 = -1.16227766 a2 = -1.16227766 Simplifying a2 = -1.16227766 Reorder the terms: 1.16227766 + a2 = -1.16227766 + 1.16227766 Combine like terms: -1.16227766 + 1.16227766 = 0.00000000 1.16227766 + 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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