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Simplifying a2 = -24 + -12a Solving a2 = -24 + -12a Solving for variable 'a'. Reorder the terms: 24 + 12a + a2 = -24 + -12a + 24 + 12a Reorder the terms: 24 + 12a + a2 = -24 + 24 + -12a + 12a Combine like terms: -24 + 24 = 0 24 + 12a + a2 = 0 + -12a + 12a 24 + 12a + a2 = -12a + 12a Combine like terms: -12a + 12a = 0 24 + 12a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 12a + -24 + a2 = 0 + -24 Reorder the terms: 24 + -24 + 12a + a2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 12a + a2 = 0 + -24 12a + a2 = 0 + -24 Combine like terms: 0 + -24 = -24 12a + a2 = -24 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 = -24 + 36 Reorder the terms: 36 + 12a + a2 = -24 + 36 Combine like terms: -24 + 36 = 12 36 + 12a + a2 = 12 Factor a perfect square on the left side: (a + 6)(a + 6) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (a + 6) equal to 3.464101615 and -3.464101615.Subproblem 1
a + 6 = 3.464101615 Simplifying a + 6 = 3.464101615 Reorder the terms: 6 + a = 3.464101615 Solving 6 + a = 3.464101615 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 = 3.464101615 + -6 Combine like terms: 6 + -6 = 0 0 + a = 3.464101615 + -6 a = 3.464101615 + -6 Combine like terms: 3.464101615 + -6 = -2.535898385 a = -2.535898385 Simplifying a = -2.535898385Subproblem 2
a + 6 = -3.464101615 Simplifying a + 6 = -3.464101615 Reorder the terms: 6 + a = -3.464101615 Solving 6 + a = -3.464101615 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 = -3.464101615 + -6 Combine like terms: 6 + -6 = 0 0 + a = -3.464101615 + -6 a = -3.464101615 + -6 Combine like terms: -3.464101615 + -6 = -9.464101615 a = -9.464101615 Simplifying a = -9.464101615Solution
The solution to the problem is based on the solutions from the subproblems. a = {-2.535898385, -9.464101615}
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