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Simplifying 11A + -13 = -7A2 Reorder the terms: -13 + 11A = -7A2 Solving -13 + 11A = -7A2 Solving for variable 'A'. Combine like terms: -7A2 + 7A2 = 0 -13 + 11A + 7A2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + 1.571428571A + A2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + 1.571428571A + 1.857142857 + A2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + 1.571428571A + A2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + 1.571428571A + A2 = 0 + 1.857142857 1.571428571A + A2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 1.571428571A + A2 = 1.857142857 The A term is 1.571428571A. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571A + 0.6173469384 + A2 = 1.857142857 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571A + A2 = 1.857142857 + 0.6173469384 Combine like terms: 1.857142857 + 0.6173469384 = 2.4744897954 0.6173469384 + 1.571428571A + A2 = 2.4744897954 Factor a perfect square on the left side: (A + 0.7857142855)(A + 0.7857142855) = 2.4744897954 Calculate the square root of the right side: 1.57305111 Break this problem into two subproblems by setting (A + 0.7857142855) equal to 1.57305111 and -1.57305111.Subproblem 1
A + 0.7857142855 = 1.57305111 Simplifying A + 0.7857142855 = 1.57305111 Reorder the terms: 0.7857142855 + A = 1.57305111 Solving 0.7857142855 + A = 1.57305111 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + A = 1.57305111 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + A = 1.57305111 + -0.7857142855 A = 1.57305111 + -0.7857142855 Combine like terms: 1.57305111 + -0.7857142855 = 0.7873368245 A = 0.7873368245 Simplifying A = 0.7873368245Subproblem 2
A + 0.7857142855 = -1.57305111 Simplifying A + 0.7857142855 = -1.57305111 Reorder the terms: 0.7857142855 + A = -1.57305111 Solving 0.7857142855 + A = -1.57305111 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + A = -1.57305111 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + A = -1.57305111 + -0.7857142855 A = -1.57305111 + -0.7857142855 Combine like terms: -1.57305111 + -0.7857142855 = -2.3587653955 A = -2.3587653955 Simplifying A = -2.3587653955Solution
The solution to the problem is based on the solutions from the subproblems. A = {0.7873368245, -2.3587653955}
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