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Simplifying A4 + 4A2 + -9 = 0 Reorder the terms: -9 + 4A2 + A4 = 0 Solving -9 + 4A2 + A4 = 0 Solving for variable 'A'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 4A2 + 9 + A4 = 0 + 9 Reorder the terms: -9 + 9 + 4A2 + A4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4A2 + A4 = 0 + 9 4A2 + A4 = 0 + 9 Combine like terms: 0 + 9 = 9 4A2 + A4 = 9 The A term is 4A2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4A2 + 4 + A4 = 9 + 4 Reorder the terms: 4 + 4A2 + A4 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + 4A2 + A4 = 13 Factor a perfect square on the left side: (A2 + 2)(A2 + 2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (A2 + 2) equal to 3.605551275 and -3.605551275.Subproblem 1
A2 + 2 = 3.605551275 Simplifying A2 + 2 = 3.605551275 Reorder the terms: 2 + A2 = 3.605551275 Solving 2 + A2 = 3.605551275 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + A2 = 3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + A2 = 3.605551275 + -2 A2 = 3.605551275 + -2 Combine like terms: 3.605551275 + -2 = 1.605551275 A2 = 1.605551275 Simplifying A2 = 1.605551275 Take the square root of each side: A = {-1.267103498, 1.267103498}Subproblem 2
A2 + 2 = -3.605551275 Simplifying A2 + 2 = -3.605551275 Reorder the terms: 2 + A2 = -3.605551275 Solving 2 + A2 = -3.605551275 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + A2 = -3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + A2 = -3.605551275 + -2 A2 = -3.605551275 + -2 Combine like terms: -3.605551275 + -2 = -5.605551275 A2 = -5.605551275 Simplifying A2 = -5.605551275 Reorder the terms: 5.605551275 + A2 = -5.605551275 + 5.605551275 Combine like terms: -5.605551275 + 5.605551275 = 0.000000000 5.605551275 + 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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