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Simplifying A2 + -8A + -1 = 0 Reorder the terms: -1 + -8A + A2 = 0 Solving -1 + -8A + A2 = 0 Solving for variable 'A'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -8A + 1 + A2 = 0 + 1 Reorder the terms: -1 + 1 + -8A + A2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8A + A2 = 0 + 1 -8A + A2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8A + A2 = 1 The A term is -8A. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8A + 16 + A2 = 1 + 16 Reorder the terms: 16 + -8A + A2 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + -8A + A2 = 17 Factor a perfect square on the left side: (A + -4)(A + -4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (A + -4) equal to 4.123105626 and -4.123105626.Subproblem 1
A + -4 = 4.123105626 Simplifying A + -4 = 4.123105626 Reorder the terms: -4 + A = 4.123105626 Solving -4 + A = 4.123105626 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + A = 4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + A = 4.123105626 + 4 A = 4.123105626 + 4 Combine like terms: 4.123105626 + 4 = 8.123105626 A = 8.123105626 Simplifying A = 8.123105626Subproblem 2
A + -4 = -4.123105626 Simplifying A + -4 = -4.123105626 Reorder the terms: -4 + A = -4.123105626 Solving -4 + A = -4.123105626 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + A = -4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + A = -4.123105626 + 4 A = -4.123105626 + 4 Combine like terms: -4.123105626 + 4 = -0.123105626 A = -0.123105626 Simplifying A = -0.123105626Solution
The solution to the problem is based on the solutions from the subproblems. A = {8.123105626, -0.123105626}
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