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Simplifying a4 + -10a2 + 9 = 18 Reorder the terms: 9 + -10a2 + a4 = 18 Solving 9 + -10a2 + a4 = 18 Solving for variable 'a'. Reorder the terms: 9 + -18 + -10a2 + a4 = 18 + -18 Combine like terms: 9 + -18 = -9 -9 + -10a2 + a4 = 18 + -18 Combine like terms: 18 + -18 = 0 -9 + -10a2 + a4 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -10a2 + 9 + a4 = 0 + 9 Reorder the terms: -9 + 9 + -10a2 + a4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -10a2 + a4 = 0 + 9 -10a2 + a4 = 0 + 9 Combine like terms: 0 + 9 = 9 -10a2 + a4 = 9 The a term is -10a2. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10a2 + 25 + a4 = 9 + 25 Reorder the terms: 25 + -10a2 + a4 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + -10a2 + a4 = 34 Factor a perfect square on the left side: (a2 + -5)(a2 + -5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (a2 + -5) equal to 5.830951895 and -5.830951895.Subproblem 1
a2 + -5 = 5.830951895 Simplifying a2 + -5 = 5.830951895 Reorder the terms: -5 + a2 = 5.830951895 Solving -5 + a2 = 5.830951895 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a2 = 5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + a2 = 5.830951895 + 5 a2 = 5.830951895 + 5 Combine like terms: 5.830951895 + 5 = 10.830951895 a2 = 10.830951895 Simplifying a2 = 10.830951895 Take the square root of each side: a = {-3.291041157, 3.291041157}Subproblem 2
a2 + -5 = -5.830951895 Simplifying a2 + -5 = -5.830951895 Reorder the terms: -5 + a2 = -5.830951895 Solving -5 + a2 = -5.830951895 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a2 = -5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + a2 = -5.830951895 + 5 a2 = -5.830951895 + 5 Combine like terms: -5.830951895 + 5 = -0.830951895 a2 = -0.830951895 Simplifying a2 = -0.830951895 Reorder the terms: 0.830951895 + a2 = -0.830951895 + 0.830951895 Combine like terms: -0.830951895 + 0.830951895 = 0.000000000 0.830951895 + 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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