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Simplifying a4 + -1a2 + 0.25 = 0 Reorder the terms: 0.25 + -1a2 + a4 = 0 Solving 0.25 + -1a2 + a4 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1a2 + -0.25 + a4 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1a2 + a4 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1a2 + a4 = 0 + -0.25 -1a2 + a4 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1a2 + a4 = -0.25 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 = -0.25 + 0.25 Reorder the terms: 0.25 + -1a2 + a4 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + -1a2 + a4 = 0.00 Factor a perfect square on the left side: (a2 + -0.5)(a2 + -0.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (a2 + -0.5) equal to 0.00 and 0.00.Subproblem 1
a2 + -0.5 = 0.00 Simplifying a2 + -0.5 = 0.00 Reorder the terms: -0.5 + a2 = 0.00 Solving -0.5 + a2 = 0.00 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 = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a2 = 0.00 + 0.5 a2 = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 a2 = 0.5 Simplifying a2 = 0.5 Take the square root of each side: a = {-0.707106781, 0.707106781}Subproblem 2
a2 + -0.5 = 0.00 Simplifying a2 + -0.5 = 0.00 Reorder the terms: -0.5 + a2 = 0.00 Solving -0.5 + a2 = 0.00 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 = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a2 = 0.00 + 0.5 a2 = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 a2 = 0.5 Simplifying a2 = 0.5 Take the square root of each side: a = {-0.707106781, 0.707106781}Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.707106781, 0.707106781, -0.707106781, 0.707106781}
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