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Simplifying a2 + 13a + -1 = 0 Reorder the terms: -1 + 13a + a2 = 0 Solving -1 + 13a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 13a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 13a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 13a + a2 = 0 + 1 13a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 13a + a2 = 1 The a term is 13a. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13a + 42.25 + a2 = 1 + 42.25 Reorder the terms: 42.25 + 13a + a2 = 1 + 42.25 Combine like terms: 1 + 42.25 = 43.25 42.25 + 13a + a2 = 43.25 Factor a perfect square on the left side: (a + 6.5)(a + 6.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (a + 6.5) equal to 6.576473219 and -6.576473219.Subproblem 1
a + 6.5 = 6.576473219 Simplifying a + 6.5 = 6.576473219 Reorder the terms: 6.5 + a = 6.576473219 Solving 6.5 + a = 6.576473219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = 6.576473219 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = 6.576473219 + -6.5 a = 6.576473219 + -6.5 Combine like terms: 6.576473219 + -6.5 = 0.076473219 a = 0.076473219 Simplifying a = 0.076473219Subproblem 2
a + 6.5 = -6.576473219 Simplifying a + 6.5 = -6.576473219 Reorder the terms: 6.5 + a = -6.576473219 Solving 6.5 + a = -6.576473219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = -6.576473219 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = -6.576473219 + -6.5 a = -6.576473219 + -6.5 Combine like terms: -6.576473219 + -6.5 = -13.076473219 a = -13.076473219 Simplifying a = -13.076473219Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.076473219, -13.076473219}
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