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Simplifying a4 + -6a2 + 4 = 0 Reorder the terms: 4 + -6a2 + a4 = 0 Solving 4 + -6a2 + a4 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6a2 + -4 + a4 = 0 + -4 Reorder the terms: 4 + -4 + -6a2 + a4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6a2 + a4 = 0 + -4 -6a2 + a4 = 0 + -4 Combine like terms: 0 + -4 = -4 -6a2 + a4 = -4 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 = -4 + 9 Reorder the terms: 9 + -6a2 + a4 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6a2 + a4 = 5 Factor a perfect square on the left side: (a2 + -3)(a2 + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (a2 + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
a2 + -3 = 2.236067978 Simplifying a2 + -3 = 2.236067978 Reorder the terms: -3 + a2 = 2.236067978 Solving -3 + a2 = 2.236067978 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 = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + a2 = 2.236067978 + 3 a2 = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 a2 = 5.236067978 Simplifying a2 = 5.236067978 Take the square root of each side: a = {-2.288245611, 2.288245611}Subproblem 2
a2 + -3 = -2.236067978 Simplifying a2 + -3 = -2.236067978 Reorder the terms: -3 + a2 = -2.236067978 Solving -3 + a2 = -2.236067978 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 = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + a2 = -2.236067978 + 3 a2 = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 a2 = 0.763932022 Simplifying a2 = 0.763932022 Take the square root of each side: a = {-0.874032049, 0.874032049}Solution
The solution to the problem is based on the solutions from the subproblems. a = {-2.288245611, 2.288245611, -0.874032049, 0.874032049}
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