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Simplifying 3a2 + 100a + -81600 = 0 Reorder the terms: -81600 + 100a + 3a2 = 0 Solving -81600 + 100a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -27200 + 33.33333333a + a2 = 0 Move the constant term to the right: Add '27200' to each side of the equation. -27200 + 33.33333333a + 27200 + a2 = 0 + 27200 Reorder the terms: -27200 + 27200 + 33.33333333a + a2 = 0 + 27200 Combine like terms: -27200 + 27200 = 0 0 + 33.33333333a + a2 = 0 + 27200 33.33333333a + a2 = 0 + 27200 Combine like terms: 0 + 27200 = 27200 33.33333333a + a2 = 27200 The a term is 33.33333333a. Take half its coefficient (16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. 33.33333333a + 277.7777779 + a2 = 27200 + 277.7777779 Reorder the terms: 277.7777779 + 33.33333333a + a2 = 27200 + 277.7777779 Combine like terms: 27200 + 277.7777779 = 27477.7777779 277.7777779 + 33.33333333a + a2 = 27477.7777779 Factor a perfect square on the left side: (a + 16.66666667)(a + 16.66666667) = 27477.7777779 Calculate the square root of the right side: 165.764223456 Break this problem into two subproblems by setting (a + 16.66666667) equal to 165.764223456 and -165.764223456.Subproblem 1
a + 16.66666667 = 165.764223456 Simplifying a + 16.66666667 = 165.764223456 Reorder the terms: 16.66666667 + a = 165.764223456 Solving 16.66666667 + a = 165.764223456 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + a = 165.764223456 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + a = 165.764223456 + -16.66666667 a = 165.764223456 + -16.66666667 Combine like terms: 165.764223456 + -16.66666667 = 149.097556786 a = 149.097556786 Simplifying a = 149.097556786Subproblem 2
a + 16.66666667 = -165.764223456 Simplifying a + 16.66666667 = -165.764223456 Reorder the terms: 16.66666667 + a = -165.764223456 Solving 16.66666667 + a = -165.764223456 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + a = -165.764223456 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + a = -165.764223456 + -16.66666667 a = -165.764223456 + -16.66666667 Combine like terms: -165.764223456 + -16.66666667 = -182.430890126 a = -182.430890126 Simplifying a = -182.430890126Solution
The solution to the problem is based on the solutions from the subproblems. a = {149.097556786, -182.430890126}
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