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Simplifying 4a2 + 800a + 4200 = 263333.33 Reorder the terms: 4200 + 800a + 4a2 = 263333.33 Solving 4200 + 800a + 4a2 = 263333.33 Solving for variable 'a'. Reorder the terms: 4200 + -263333.33 + 800a + 4a2 = 263333.33 + -263333.33 Combine like terms: 4200 + -263333.33 = -259133.33 -259133.33 + 800a + 4a2 = 263333.33 + -263333.33 Combine like terms: 263333.33 + -263333.33 = 0.00 -259133.33 + 800a + 4a2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -64783.3325 + 200a + a2 = 0.00 Move the constant term to the right: Add '64783.3325' to each side of the equation. -64783.3325 + 200a + 64783.3325 + a2 = 0.00 + 64783.3325 Reorder the terms: -64783.3325 + 64783.3325 + 200a + a2 = 0.00 + 64783.3325 Combine like terms: -64783.3325 + 64783.3325 = 0.0000 0.0000 + 200a + a2 = 0.00 + 64783.3325 200a + a2 = 0.00 + 64783.3325 Combine like terms: 0.00 + 64783.3325 = 64783.3325 200a + a2 = 64783.3325 The a term is 200a. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200a + 10000 + a2 = 64783.3325 + 10000 Reorder the terms: 10000 + 200a + a2 = 64783.3325 + 10000 Combine like terms: 64783.3325 + 10000 = 74783.3325 10000 + 200a + a2 = 74783.3325 Factor a perfect square on the left side: (a + 100)(a + 100) = 74783.3325 Calculate the square root of the right side: 273.465413718 Break this problem into two subproblems by setting (a + 100) equal to 273.465413718 and -273.465413718.Subproblem 1
a + 100 = 273.465413718 Simplifying a + 100 = 273.465413718 Reorder the terms: 100 + a = 273.465413718 Solving 100 + a = 273.465413718 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + a = 273.465413718 + -100 Combine like terms: 100 + -100 = 0 0 + a = 273.465413718 + -100 a = 273.465413718 + -100 Combine like terms: 273.465413718 + -100 = 173.465413718 a = 173.465413718 Simplifying a = 173.465413718Subproblem 2
a + 100 = -273.465413718 Simplifying a + 100 = -273.465413718 Reorder the terms: 100 + a = -273.465413718 Solving 100 + a = -273.465413718 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + a = -273.465413718 + -100 Combine like terms: 100 + -100 = 0 0 + a = -273.465413718 + -100 a = -273.465413718 + -100 Combine like terms: -273.465413718 + -100 = -373.465413718 a = -373.465413718 Simplifying a = -373.465413718Solution
The solution to the problem is based on the solutions from the subproblems. a = {173.465413718, -373.465413718}
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