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Simplifying a4 + -2a2 = 0.5625 Reorder the terms: -2a2 + a4 = 0.5625 Solving -2a2 + a4 = 0.5625 Solving for variable 'a'. Reorder the terms: -0.5625 + -2a2 + a4 = 0.5625 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 -0.5625 + -2a2 + a4 = 0.0000 Begin completing the square. Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -2a2 + 0.5625 + a4 = 0.0000 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -2a2 + a4 = 0.0000 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -2a2 + a4 = 0.0000 + 0.5625 -2a2 + a4 = 0.0000 + 0.5625 Combine like terms: 0.0000 + 0.5625 = 0.5625 -2a2 + a4 = 0.5625 The a term is -2a2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a2 + 1 + a4 = 0.5625 + 1 Reorder the terms: 1 + -2a2 + a4 = 0.5625 + 1 Combine like terms: 0.5625 + 1 = 1.5625 1 + -2a2 + a4 = 1.5625 Factor a perfect square on the left side: (a2 + -1)(a2 + -1) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (a2 + -1) equal to 1.25 and -1.25.Subproblem 1
a2 + -1 = 1.25 Simplifying a2 + -1 = 1.25 Reorder the terms: -1 + a2 = 1.25 Solving -1 + a2 = 1.25 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a2 = 1.25 + 1 Combine like terms: -1 + 1 = 0 0 + a2 = 1.25 + 1 a2 = 1.25 + 1 Combine like terms: 1.25 + 1 = 2.25 a2 = 2.25 Simplifying a2 = 2.25 Take the square root of each side: a = {-1.5, 1.5}Subproblem 2
a2 + -1 = -1.25 Simplifying a2 + -1 = -1.25 Reorder the terms: -1 + a2 = -1.25 Solving -1 + a2 = -1.25 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a2 = -1.25 + 1 Combine like terms: -1 + 1 = 0 0 + a2 = -1.25 + 1 a2 = -1.25 + 1 Combine like terms: -1.25 + 1 = -0.25 a2 = -0.25 Simplifying a2 = -0.25 Reorder the terms: 0.25 + a2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + a2 = 0.00 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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