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Simplifying 2a2 + -1a + -12 = 2 Reorder the terms: -12 + -1a + 2a2 = 2 Solving -12 + -1a + 2a2 = 2 Solving for variable 'a'. Reorder the terms: -12 + -2 + -1a + 2a2 = 2 + -2 Combine like terms: -12 + -2 = -14 -14 + -1a + 2a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -14 + -1a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + -0.5a + a2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.5a + 7 + a2 = 0 + 7 Reorder the terms: -7 + 7 + -0.5a + a2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.5a + a2 = 0 + 7 -0.5a + a2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.5a + a2 = 7 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 = 7 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = 7 + 0.0625 Combine like terms: 7 + 0.0625 = 7.0625 0.0625 + -0.5a + a2 = 7.0625 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (a + -0.25) equal to 2.657536453 and -2.657536453.Subproblem 1
a + -0.25 = 2.657536453 Simplifying a + -0.25 = 2.657536453 Reorder the terms: -0.25 + a = 2.657536453 Solving -0.25 + a = 2.657536453 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 = 2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 2.657536453 + 0.25 a = 2.657536453 + 0.25 Combine like terms: 2.657536453 + 0.25 = 2.907536453 a = 2.907536453 Simplifying a = 2.907536453Subproblem 2
a + -0.25 = -2.657536453 Simplifying a + -0.25 = -2.657536453 Reorder the terms: -0.25 + a = -2.657536453 Solving -0.25 + a = -2.657536453 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 = -2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -2.657536453 + 0.25 a = -2.657536453 + 0.25 Combine like terms: -2.657536453 + 0.25 = -2.407536453 a = -2.407536453 Simplifying a = -2.407536453Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.907536453, -2.407536453}
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