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Simplifying a2 + 12a + -94 = 0 Reorder the terms: -94 + 12a + a2 = 0 Solving -94 + 12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + 12a + 94 + a2 = 0 + 94 Reorder the terms: -94 + 94 + 12a + a2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 12a + a2 = 0 + 94 12a + a2 = 0 + 94 Combine like terms: 0 + 94 = 94 12a + a2 = 94 The a term is 12a. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12a + 36 + a2 = 94 + 36 Reorder the terms: 36 + 12a + a2 = 94 + 36 Combine like terms: 94 + 36 = 130 36 + 12a + a2 = 130 Factor a perfect square on the left side: (a + 6)(a + 6) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (a + 6) equal to 11.401754251 and -11.401754251.Subproblem 1
a + 6 = 11.401754251 Simplifying a + 6 = 11.401754251 Reorder the terms: 6 + a = 11.401754251 Solving 6 + a = 11.401754251 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 11.401754251 + -6 Combine like terms: 6 + -6 = 0 0 + a = 11.401754251 + -6 a = 11.401754251 + -6 Combine like terms: 11.401754251 + -6 = 5.401754251 a = 5.401754251 Simplifying a = 5.401754251Subproblem 2
a + 6 = -11.401754251 Simplifying a + 6 = -11.401754251 Reorder the terms: 6 + a = -11.401754251 Solving 6 + a = -11.401754251 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = -11.401754251 + -6 Combine like terms: 6 + -6 = 0 0 + a = -11.401754251 + -6 a = -11.401754251 + -6 Combine like terms: -11.401754251 + -6 = -17.401754251 a = -17.401754251 Simplifying a = -17.401754251Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.401754251, -17.401754251}
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