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Simplifying 2a2 + 17a + 6 = 0 Reorder the terms: 6 + 17a + 2a2 = 0 Solving 6 + 17a + 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'. 3 + 8.5a + a2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 8.5a + -3 + a2 = 0 + -3 Reorder the terms: 3 + -3 + 8.5a + a2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8.5a + a2 = 0 + -3 8.5a + a2 = 0 + -3 Combine like terms: 0 + -3 = -3 8.5a + a2 = -3 The a term is 8.5a. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5a + 18.0625 + a2 = -3 + 18.0625 Reorder the terms: 18.0625 + 8.5a + a2 = -3 + 18.0625 Combine like terms: -3 + 18.0625 = 15.0625 18.0625 + 8.5a + a2 = 15.0625 Factor a perfect square on the left side: (a + 4.25)(a + 4.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (a + 4.25) equal to 3.881043674 and -3.881043674.Subproblem 1
a + 4.25 = 3.881043674 Simplifying a + 4.25 = 3.881043674 Reorder the terms: 4.25 + a = 3.881043674 Solving 4.25 + a = 3.881043674 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + a = 3.881043674 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + a = 3.881043674 + -4.25 a = 3.881043674 + -4.25 Combine like terms: 3.881043674 + -4.25 = -0.368956326 a = -0.368956326 Simplifying a = -0.368956326Subproblem 2
a + 4.25 = -3.881043674 Simplifying a + 4.25 = -3.881043674 Reorder the terms: 4.25 + a = -3.881043674 Solving 4.25 + a = -3.881043674 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + a = -3.881043674 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + a = -3.881043674 + -4.25 a = -3.881043674 + -4.25 Combine like terms: -3.881043674 + -4.25 = -8.131043674 a = -8.131043674 Simplifying a = -8.131043674Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.368956326, -8.131043674}
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