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Simplifying 5a2 + 16a + -12 = 0 Reorder the terms: -12 + 16a + 5a2 = 0 Solving -12 + 16a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 3.2a + a2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 3.2a + 2.4 + a2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 3.2a + a2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 3.2a + a2 = 0 + 2.4 3.2a + a2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 3.2a + a2 = 2.4 The a term is 3.2a. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2a + 2.56 + a2 = 2.4 + 2.56 Reorder the terms: 2.56 + 3.2a + a2 = 2.4 + 2.56 Combine like terms: 2.4 + 2.56 = 4.96 2.56 + 3.2a + a2 = 4.96 Factor a perfect square on the left side: (a + 1.6)(a + 1.6) = 4.96 Calculate the square root of the right side: 2.227105745 Break this problem into two subproblems by setting (a + 1.6) equal to 2.227105745 and -2.227105745.Subproblem 1
a + 1.6 = 2.227105745 Simplifying a + 1.6 = 2.227105745 Reorder the terms: 1.6 + a = 2.227105745 Solving 1.6 + a = 2.227105745 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + a = 2.227105745 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + a = 2.227105745 + -1.6 a = 2.227105745 + -1.6 Combine like terms: 2.227105745 + -1.6 = 0.627105745 a = 0.627105745 Simplifying a = 0.627105745Subproblem 2
a + 1.6 = -2.227105745 Simplifying a + 1.6 = -2.227105745 Reorder the terms: 1.6 + a = -2.227105745 Solving 1.6 + a = -2.227105745 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + a = -2.227105745 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + a = -2.227105745 + -1.6 a = -2.227105745 + -1.6 Combine like terms: -2.227105745 + -1.6 = -3.827105745 a = -3.827105745 Simplifying a = -3.827105745Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.627105745, -3.827105745}
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