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Simplifying 2a2 + 13a + -26 = 0 Reorder the terms: -26 + 13a + 2a2 = 0 Solving -26 + 13a + 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'. -13 + 6.5a + a2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 6.5a + 13 + a2 = 0 + 13 Reorder the terms: -13 + 13 + 6.5a + a2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 6.5a + a2 = 0 + 13 6.5a + a2 = 0 + 13 Combine like terms: 0 + 13 = 13 6.5a + a2 = 13 The a term is 6.5a. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5a + 10.5625 + a2 = 13 + 10.5625 Reorder the terms: 10.5625 + 6.5a + a2 = 13 + 10.5625 Combine like terms: 13 + 10.5625 = 23.5625 10.5625 + 6.5a + a2 = 23.5625 Factor a perfect square on the left side: (a + 3.25)(a + 3.25) = 23.5625 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (a + 3.25) equal to 4.85412196 and -4.85412196.Subproblem 1
a + 3.25 = 4.85412196 Simplifying a + 3.25 = 4.85412196 Reorder the terms: 3.25 + a = 4.85412196 Solving 3.25 + a = 4.85412196 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + a = 4.85412196 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + a = 4.85412196 + -3.25 a = 4.85412196 + -3.25 Combine like terms: 4.85412196 + -3.25 = 1.60412196 a = 1.60412196 Simplifying a = 1.60412196Subproblem 2
a + 3.25 = -4.85412196 Simplifying a + 3.25 = -4.85412196 Reorder the terms: 3.25 + a = -4.85412196 Solving 3.25 + a = -4.85412196 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + a = -4.85412196 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + a = -4.85412196 + -3.25 a = -4.85412196 + -3.25 Combine like terms: -4.85412196 + -3.25 = -8.10412196 a = -8.10412196 Simplifying a = -8.10412196Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.60412196, -8.10412196}
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