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Simplifying (9a2) + 4a = 500 Reorder the terms: 4a + (9a2) = 500 Solving 4a + (9a2) = 500 Solving for variable 'a'. Reorder the terms: -500 + 4a + (9a2) = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 4a + (9a2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -55.55555556 + 0.4444444444a + a2 = 0 Move the constant term to the right: Add '55.55555556' to each side of the equation. -55.55555556 + 0.4444444444a + 55.55555556 + a2 = 0 + 55.55555556 Reorder the terms: -55.55555556 + 55.55555556 + 0.4444444444a + a2 = 0 + 55.55555556 Combine like terms: -55.55555556 + 55.55555556 = 0.00000000 0.00000000 + 0.4444444444a + a2 = 0 + 55.55555556 0.4444444444a + a2 = 0 + 55.55555556 Combine like terms: 0 + 55.55555556 = 55.55555556 0.4444444444a + a2 = 55.55555556 The a term is 0.4444444444a. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444a + 0.04938271604 + a2 = 55.55555556 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444a + a2 = 55.55555556 + 0.04938271604 Combine like terms: 55.55555556 + 0.04938271604 = 55.60493827604 0.04938271604 + 0.4444444444a + a2 = 55.60493827604 Factor a perfect square on the left side: ((a) + 0.2222222222)((a) + 0.2222222222) = 55.60493827604 Calculate the square root of the right side: 7.456871883 Break this problem into two subproblems by setting ((a) + 0.2222222222) equal to 7.456871883 and -7.456871883.Subproblem 1
(a) + 0.2222222222 = 7.456871883 Simplifying (a) + 0.2222222222 = 7.456871883 a + 0.2222222222 = 7.456871883 Reorder the terms: 0.2222222222 + a = 7.456871883 Solving 0.2222222222 + a = 7.456871883 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + a = 7.456871883 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + a = 7.456871883 + -0.2222222222 a = 7.456871883 + -0.2222222222 Combine like terms: 7.456871883 + -0.2222222222 = 7.2346496608 a = 7.2346496608 Simplifying a = 7.2346496608Subproblem 2
(a) + 0.2222222222 = -7.456871883 Simplifying (a) + 0.2222222222 = -7.456871883 a + 0.2222222222 = -7.456871883 Reorder the terms: 0.2222222222 + a = -7.456871883 Solving 0.2222222222 + a = -7.456871883 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + a = -7.456871883 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + a = -7.456871883 + -0.2222222222 a = -7.456871883 + -0.2222222222 Combine like terms: -7.456871883 + -0.2222222222 = -7.6790941052 a = -7.6790941052 Simplifying a = -7.6790941052Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.2346496608, -7.6790941052}
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