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Simplifying 3a4 + 4 * 3a2 + -7 = 0 Multiply 4 * 3 3a4 + 12a2 + -7 = 0 Reorder the terms: -7 + 12a2 + 3a4 = 0 Solving -7 + 12a2 + 3a4 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 4a2 + a4 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 4a2 + 2.333333333 + a4 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 4a2 + a4 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 4a2 + a4 = 0 + 2.333333333 4a2 + a4 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 4a2 + a4 = 2.333333333 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 = 2.333333333 + 4 Reorder the terms: 4 + 4a2 + a4 = 2.333333333 + 4 Combine like terms: 2.333333333 + 4 = 6.333333333 4 + 4a2 + a4 = 6.333333333 Factor a perfect square on the left side: (a2 + 2)(a2 + 2) = 6.333333333 Calculate the square root of the right side: 2.516611478 Break this problem into two subproblems by setting (a2 + 2) equal to 2.516611478 and -2.516611478.Subproblem 1
a2 + 2 = 2.516611478 Simplifying a2 + 2 = 2.516611478 Reorder the terms: 2 + a2 = 2.516611478 Solving 2 + a2 = 2.516611478 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 = 2.516611478 + -2 Combine like terms: 2 + -2 = 0 0 + a2 = 2.516611478 + -2 a2 = 2.516611478 + -2 Combine like terms: 2.516611478 + -2 = 0.516611478 a2 = 0.516611478 Simplifying a2 = 0.516611478 Take the square root of each side: a = {-0.718756898, 0.718756898}Subproblem 2
a2 + 2 = -2.516611478 Simplifying a2 + 2 = -2.516611478 Reorder the terms: 2 + a2 = -2.516611478 Solving 2 + a2 = -2.516611478 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 = -2.516611478 + -2 Combine like terms: 2 + -2 = 0 0 + a2 = -2.516611478 + -2 a2 = -2.516611478 + -2 Combine like terms: -2.516611478 + -2 = -4.516611478 a2 = -4.516611478 Simplifying a2 = -4.516611478 Reorder the terms: 4.516611478 + a2 = -4.516611478 + 4.516611478 Combine like terms: -4.516611478 + 4.516611478 = 0.000000000 4.516611478 + a2 = 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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