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Simplifying a4 + -8a2 + 13 = 0 Reorder the terms: 13 + -8a2 + a4 = 0 Solving 13 + -8a2 + a4 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8a2 + -13 + a4 = 0 + -13 Reorder the terms: 13 + -13 + -8a2 + a4 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8a2 + a4 = 0 + -13 -8a2 + a4 = 0 + -13 Combine like terms: 0 + -13 = -13 -8a2 + a4 = -13 The a term is -8a2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a2 + 16 + a4 = -13 + 16 Reorder the terms: 16 + -8a2 + a4 = -13 + 16 Combine like terms: -13 + 16 = 3 16 + -8a2 + a4 = 3 Factor a perfect square on the left side: (a2 + -4)(a2 + -4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (a2 + -4) equal to 1.732050808 and -1.732050808.Subproblem 1
a2 + -4 = 1.732050808 Simplifying a2 + -4 = 1.732050808 Reorder the terms: -4 + a2 = 1.732050808 Solving -4 + a2 = 1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a2 = 1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + a2 = 1.732050808 + 4 a2 = 1.732050808 + 4 Combine like terms: 1.732050808 + 4 = 5.732050808 a2 = 5.732050808 Simplifying a2 = 5.732050808 Take the square root of each side: a = {-2.394170171, 2.394170171}Subproblem 2
a2 + -4 = -1.732050808 Simplifying a2 + -4 = -1.732050808 Reorder the terms: -4 + a2 = -1.732050808 Solving -4 + a2 = -1.732050808 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a2 = -1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + a2 = -1.732050808 + 4 a2 = -1.732050808 + 4 Combine like terms: -1.732050808 + 4 = 2.267949192 a2 = 2.267949192 Simplifying a2 = 2.267949192 Take the square root of each side: a = {-1.505971179, 1.505971179}Solution
The solution to the problem is based on the solutions from the subproblems. a = {-2.394170171, 2.394170171, -1.505971179, 1.505971179}
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