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Simplifying 10A2 + -2A + -3 = 0 Reorder the terms: -3 + -2A + 10A2 = 0 Solving -3 + -2A + 10A2 = 0 Solving for variable 'A'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -0.2A + A2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.2A + 0.3 + A2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.2A + A2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.2A + A2 = 0 + 0.3 -0.2A + A2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -0.2A + A2 = 0.3 The A term is -0.2A. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2A + 0.01 + A2 = 0.3 + 0.01 Reorder the terms: 0.01 + -0.2A + A2 = 0.3 + 0.01 Combine like terms: 0.3 + 0.01 = 0.31 0.01 + -0.2A + A2 = 0.31 Factor a perfect square on the left side: (A + -0.1)(A + -0.1) = 0.31 Calculate the square root of the right side: 0.556776436 Break this problem into two subproblems by setting (A + -0.1) equal to 0.556776436 and -0.556776436.Subproblem 1
A + -0.1 = 0.556776436 Simplifying A + -0.1 = 0.556776436 Reorder the terms: -0.1 + A = 0.556776436 Solving -0.1 + A = 0.556776436 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + A = 0.556776436 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + A = 0.556776436 + 0.1 A = 0.556776436 + 0.1 Combine like terms: 0.556776436 + 0.1 = 0.656776436 A = 0.656776436 Simplifying A = 0.656776436Subproblem 2
A + -0.1 = -0.556776436 Simplifying A + -0.1 = -0.556776436 Reorder the terms: -0.1 + A = -0.556776436 Solving -0.1 + A = -0.556776436 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + A = -0.556776436 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + A = -0.556776436 + 0.1 A = -0.556776436 + 0.1 Combine like terms: -0.556776436 + 0.1 = -0.456776436 A = -0.456776436 Simplifying A = -0.456776436Solution
The solution to the problem is based on the solutions from the subproblems. A = {0.656776436, -0.456776436}
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