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Simplifying 8a4 + -8a2 = 9 Reorder the terms: -8a2 + 8a4 = 9 Solving -8a2 + 8a4 = 9 Solving for variable 'a'. Reorder the terms: -9 + -8a2 + 8a4 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -8a2 + 8a4 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -1a2 + a4 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -1a2 + 1.125 + a4 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -1a2 + a4 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -1a2 + a4 = 0 + 1.125 -1a2 + a4 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -1a2 + a4 = 1.125 The a term is -1a2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a2 + 0.25 + a4 = 1.125 + 0.25 Reorder the terms: 0.25 + -1a2 + a4 = 1.125 + 0.25 Combine like terms: 1.125 + 0.25 = 1.375 0.25 + -1a2 + a4 = 1.375 Factor a perfect square on the left side: (a2 + -0.5)(a2 + -0.5) = 1.375 Calculate the square root of the right side: 1.17260394 Break this problem into two subproblems by setting (a2 + -0.5) equal to 1.17260394 and -1.17260394.Subproblem 1
a2 + -0.5 = 1.17260394 Simplifying a2 + -0.5 = 1.17260394 Reorder the terms: -0.5 + a2 = 1.17260394 Solving -0.5 + a2 = 1.17260394 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a2 = 1.17260394 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a2 = 1.17260394 + 0.5 a2 = 1.17260394 + 0.5 Combine like terms: 1.17260394 + 0.5 = 1.67260394 a2 = 1.67260394 Simplifying a2 = 1.67260394 Take the square root of each side: a = {-1.293291901, 1.293291901}Subproblem 2
a2 + -0.5 = -1.17260394 Simplifying a2 + -0.5 = -1.17260394 Reorder the terms: -0.5 + a2 = -1.17260394 Solving -0.5 + a2 = -1.17260394 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a2 = -1.17260394 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a2 = -1.17260394 + 0.5 a2 = -1.17260394 + 0.5 Combine like terms: -1.17260394 + 0.5 = -0.67260394 a2 = -0.67260394 Simplifying a2 = -0.67260394 Reorder the terms: 0.67260394 + a2 = -0.67260394 + 0.67260394 Combine like terms: -0.67260394 + 0.67260394 = 0.00000000 0.67260394 + 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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