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Simplifying A2 + 12A = 54 Reorder the terms: 12A + A2 = 54 Solving 12A + A2 = 54 Solving for variable 'A'. Reorder the terms: -54 + 12A + A2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 12A + A2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 12A + 54 + A2 = 0 + 54 Reorder the terms: -54 + 54 + 12A + A2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 12A + A2 = 0 + 54 12A + A2 = 0 + 54 Combine like terms: 0 + 54 = 54 12A + A2 = 54 The A term is 12A. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12A + 36 + A2 = 54 + 36 Reorder the terms: 36 + 12A + A2 = 54 + 36 Combine like terms: 54 + 36 = 90 36 + 12A + A2 = 90 Factor a perfect square on the left side: (A + 6)(A + 6) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (A + 6) equal to 9.486832981 and -9.486832981.Subproblem 1
A + 6 = 9.486832981 Simplifying A + 6 = 9.486832981 Reorder the terms: 6 + A = 9.486832981 Solving 6 + A = 9.486832981 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + A = 9.486832981 + -6 Combine like terms: 6 + -6 = 0 0 + A = 9.486832981 + -6 A = 9.486832981 + -6 Combine like terms: 9.486832981 + -6 = 3.486832981 A = 3.486832981 Simplifying A = 3.486832981Subproblem 2
A + 6 = -9.486832981 Simplifying A + 6 = -9.486832981 Reorder the terms: 6 + A = -9.486832981 Solving 6 + A = -9.486832981 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + A = -9.486832981 + -6 Combine like terms: 6 + -6 = 0 0 + A = -9.486832981 + -6 A = -9.486832981 + -6 Combine like terms: -9.486832981 + -6 = -15.486832981 A = -15.486832981 Simplifying A = -15.486832981Solution
The solution to the problem is based on the solutions from the subproblems. A = {3.486832981, -15.486832981}
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