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Simplifying 129 = 0.006A2 + -0.02A + 120 Reorder the terms: 129 = 120 + -0.02A + 0.006A2 Solving 129 = 120 + -0.02A + 0.006A2 Solving for variable 'A'. Combine like terms: 129 + -120 = 9 9 + 0.02A + -0.006A2 = 120 + -0.02A + 0.006A2 + -120 + 0.02A + -0.006A2 Reorder the terms: 9 + 0.02A + -0.006A2 = 120 + -120 + -0.02A + 0.02A + 0.006A2 + -0.006A2 Combine like terms: 120 + -120 = 0 9 + 0.02A + -0.006A2 = 0 + -0.02A + 0.02A + 0.006A2 + -0.006A2 9 + 0.02A + -0.006A2 = -0.02A + 0.02A + 0.006A2 + -0.006A2 Combine like terms: -0.02A + 0.02A = 0.00 9 + 0.02A + -0.006A2 = 0.00 + 0.006A2 + -0.006A2 9 + 0.02A + -0.006A2 = 0.006A2 + -0.006A2 Combine like terms: 0.006A2 + -0.006A2 = 0.000 9 + 0.02A + -0.006A2 = 0.000 Begin completing the square. Divide all terms by -0.006 the coefficient of the squared term: Divide each side by '-0.006'. -1500 + -3.333333333A + A2 = 0 Move the constant term to the right: Add '1500' to each side of the equation. -1500 + -3.333333333A + 1500 + A2 = 0 + 1500 Reorder the terms: -1500 + 1500 + -3.333333333A + A2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + -3.333333333A + A2 = 0 + 1500 -3.333333333A + A2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 -3.333333333A + A2 = 1500 The A term is -3.333333333A. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333A + 2.777777779 + A2 = 1500 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333A + A2 = 1500 + 2.777777779 Combine like terms: 1500 + 2.777777779 = 1502.777777779 2.777777779 + -3.333333333A + A2 = 1502.777777779 Factor a perfect square on the left side: (A + -1.666666667)(A + -1.666666667) = 1502.777777779 Calculate the square root of the right side: 38.765677832 Break this problem into two subproblems by setting (A + -1.666666667) equal to 38.765677832 and -38.765677832.Subproblem 1
A + -1.666666667 = 38.765677832 Simplifying A + -1.666666667 = 38.765677832 Reorder the terms: -1.666666667 + A = 38.765677832 Solving -1.666666667 + A = 38.765677832 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + A = 38.765677832 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + A = 38.765677832 + 1.666666667 A = 38.765677832 + 1.666666667 Combine like terms: 38.765677832 + 1.666666667 = 40.432344499 A = 40.432344499 Simplifying A = 40.432344499Subproblem 2
A + -1.666666667 = -38.765677832 Simplifying A + -1.666666667 = -38.765677832 Reorder the terms: -1.666666667 + A = -38.765677832 Solving -1.666666667 + A = -38.765677832 Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + A = -38.765677832 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + A = -38.765677832 + 1.666666667 A = -38.765677832 + 1.666666667 Combine like terms: -38.765677832 + 1.666666667 = -37.099011165 A = -37.099011165 Simplifying A = -37.099011165Solution
The solution to the problem is based on the solutions from the subproblems. A = {40.432344499, -37.099011165}
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