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Simplifying (A2) + 1296A + 4096 = 0 A2 + 1296A + 4096 = 0 Reorder the terms: 4096 + 1296A + A2 = 0 Solving 4096 + 1296A + A2 = 0 Solving for variable 'A'. Begin completing the square. Move the constant term to the right: Add '-4096' to each side of the equation. 4096 + 1296A + -4096 + A2 = 0 + -4096 Reorder the terms: 4096 + -4096 + 1296A + A2 = 0 + -4096 Combine like terms: 4096 + -4096 = 0 0 + 1296A + A2 = 0 + -4096 1296A + A2 = 0 + -4096 Combine like terms: 0 + -4096 = -4096 1296A + A2 = -4096 The A term is 1296A. Take half its coefficient (648). Square it (419904) and add it to both sides. Add '419904' to each side of the equation. 1296A + 419904 + A2 = -4096 + 419904 Reorder the terms: 419904 + 1296A + A2 = -4096 + 419904 Combine like terms: -4096 + 419904 = 415808 419904 + 1296A + A2 = 415808 Factor a perfect square on the left side: (A + 648)(A + 648) = 415808 Calculate the square root of the right side: 644.831761004 Break this problem into two subproblems by setting (A + 648) equal to 644.831761004 and -644.831761004.Subproblem 1
A + 648 = 644.831761004 Simplifying A + 648 = 644.831761004 Reorder the terms: 648 + A = 644.831761004 Solving 648 + A = 644.831761004 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-648' to each side of the equation. 648 + -648 + A = 644.831761004 + -648 Combine like terms: 648 + -648 = 0 0 + A = 644.831761004 + -648 A = 644.831761004 + -648 Combine like terms: 644.831761004 + -648 = -3.168238996 A = -3.168238996 Simplifying A = -3.168238996Subproblem 2
A + 648 = -644.831761004 Simplifying A + 648 = -644.831761004 Reorder the terms: 648 + A = -644.831761004 Solving 648 + A = -644.831761004 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-648' to each side of the equation. 648 + -648 + A = -644.831761004 + -648 Combine like terms: 648 + -648 = 0 0 + A = -644.831761004 + -648 A = -644.831761004 + -648 Combine like terms: -644.831761004 + -648 = -1292.831761004 A = -1292.831761004 Simplifying A = -1292.831761004Solution
The solution to the problem is based on the solutions from the subproblems. A = {-3.168238996, -1292.831761004}
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