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Simplifying 24a4 + -4a2 = 1 Reorder the terms: -4a2 + 24a4 = 1 Solving -4a2 + 24a4 = 1 Solving for variable 'a'. Reorder the terms: -1 + -4a2 + 24a4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -4a2 + 24a4 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.04166666667 + -0.1666666667a2 + a4 = 0 Move the constant term to the right: Add '0.04166666667' to each side of the equation. -0.04166666667 + -0.1666666667a2 + 0.04166666667 + a4 = 0 + 0.04166666667 Reorder the terms: -0.04166666667 + 0.04166666667 + -0.1666666667a2 + a4 = 0 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + -0.1666666667a2 + a4 = 0 + 0.04166666667 -0.1666666667a2 + a4 = 0 + 0.04166666667 Combine like terms: 0 + 0.04166666667 = 0.04166666667 -0.1666666667a2 + a4 = 0.04166666667 The a term is -0.1666666667a2. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667a2 + 0.006944444447 + a4 = 0.04166666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667a2 + a4 = 0.04166666667 + 0.006944444447 Combine like terms: 0.04166666667 + 0.006944444447 = 0.048611111117 0.006944444447 + -0.1666666667a2 + a4 = 0.048611111117 Factor a perfect square on the left side: (a2 + -0.08333333335)(a2 + -0.08333333335) = 0.048611111117 Calculate the square root of the right side: 0.220479276 Break this problem into two subproblems by setting (a2 + -0.08333333335) equal to 0.220479276 and -0.220479276.Subproblem 1
a2 + -0.08333333335 = 0.220479276 Simplifying a2 + -0.08333333335 = 0.220479276 Reorder the terms: -0.08333333335 + a2 = 0.220479276 Solving -0.08333333335 + a2 = 0.220479276 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + a2 = 0.220479276 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + a2 = 0.220479276 + 0.08333333335 a2 = 0.220479276 + 0.08333333335 Combine like terms: 0.220479276 + 0.08333333335 = 0.30381260935 a2 = 0.30381260935 Simplifying a2 = 0.30381260935 Take the square root of each side: a = {-0.55119199, 0.55119199}Subproblem 2
a2 + -0.08333333335 = -0.220479276 Simplifying a2 + -0.08333333335 = -0.220479276 Reorder the terms: -0.08333333335 + a2 = -0.220479276 Solving -0.08333333335 + a2 = -0.220479276 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + a2 = -0.220479276 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + a2 = -0.220479276 + 0.08333333335 a2 = -0.220479276 + 0.08333333335 Combine like terms: -0.220479276 + 0.08333333335 = -0.13714594265 a2 = -0.13714594265 Simplifying a2 = -0.13714594265 Reorder the terms: 0.13714594265 + a2 = -0.13714594265 + 0.13714594265 Combine like terms: -0.13714594265 + 0.13714594265 = 0.00000000000 0.13714594265 + a2 = 0.00000000000 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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