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Simplifying 4A + 5 = A2 + 3A Reorder the terms: 5 + 4A = A2 + 3A Reorder the terms: 5 + 4A = 3A + A2 Solving 5 + 4A = 3A + A2 Solving for variable 'A'. Combine like terms: 4A + -3A = 1A 5 + 1A + -1A2 = 3A + A2 + -3A + -1A2 Reorder the terms: 5 + 1A + -1A2 = 3A + -3A + A2 + -1A2 Combine like terms: 3A + -3A = 0 5 + 1A + -1A2 = 0 + A2 + -1A2 5 + 1A + -1A2 = A2 + -1A2 Combine like terms: A2 + -1A2 = 0 5 + 1A + -1A2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -1A + A2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1A + 5 + A2 = 0 + 5 Reorder the terms: -5 + 5 + -1A + A2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1A + A2 = 0 + 5 -1A + A2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1A + A2 = 5 The A term is -1A. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1A + 0.25 + A2 = 5 + 0.25 Reorder the terms: 0.25 + -1A + A2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1A + A2 = 5.25 Factor a perfect square on the left side: (A + -0.5)(A + -0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (A + -0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
A + -0.5 = 2.291287847 Simplifying A + -0.5 = 2.291287847 Reorder the terms: -0.5 + A = 2.291287847 Solving -0.5 + A = 2.291287847 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + A = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + A = 2.291287847 + 0.5 A = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 A = 2.791287847 Simplifying A = 2.791287847Subproblem 2
A + -0.5 = -2.291287847 Simplifying A + -0.5 = -2.291287847 Reorder the terms: -0.5 + A = -2.291287847 Solving -0.5 + A = -2.291287847 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + A = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + A = -2.291287847 + 0.5 A = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 A = -1.791287847 Simplifying A = -1.791287847Solution
The solution to the problem is based on the solutions from the subproblems. A = {2.791287847, -1.791287847}
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