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Simplifying 2a2 + -1a + -288 = 0 Reorder the terms: -288 + -1a + 2a2 = 0 Solving -288 + -1a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -144 + -0.5a + a2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + -0.5a + 144 + a2 = 0 + 144 Reorder the terms: -144 + 144 + -0.5a + a2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -0.5a + a2 = 0 + 144 -0.5a + a2 = 0 + 144 Combine like terms: 0 + 144 = 144 -0.5a + a2 = 144 The a term is -0.5a. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a + 0.0625 + a2 = 144 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = 144 + 0.0625 Combine like terms: 144 + 0.0625 = 144.0625 0.0625 + -0.5a + a2 = 144.0625 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = 144.0625 Calculate the square root of the right side: 12.002603884 Break this problem into two subproblems by setting (a + -0.25) equal to 12.002603884 and -12.002603884.Subproblem 1
a + -0.25 = 12.002603884 Simplifying a + -0.25 = 12.002603884 Reorder the terms: -0.25 + a = 12.002603884 Solving -0.25 + a = 12.002603884 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 12.002603884 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 12.002603884 + 0.25 a = 12.002603884 + 0.25 Combine like terms: 12.002603884 + 0.25 = 12.252603884 a = 12.252603884 Simplifying a = 12.252603884Subproblem 2
a + -0.25 = -12.002603884 Simplifying a + -0.25 = -12.002603884 Reorder the terms: -0.25 + a = -12.002603884 Solving -0.25 + a = -12.002603884 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -12.002603884 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -12.002603884 + 0.25 a = -12.002603884 + 0.25 Combine like terms: -12.002603884 + 0.25 = -11.752603884 a = -11.752603884 Simplifying a = -11.752603884Solution
The solution to the problem is based on the solutions from the subproblems. a = {12.252603884, -11.752603884}
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