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Simplifying a2 + -12a + -12 = 0 Reorder the terms: -12 + -12a + a2 = 0 Solving -12 + -12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -12a + 12 + a2 = 0 + 12 Reorder the terms: -12 + 12 + -12a + a2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -12a + a2 = 0 + 12 -12a + a2 = 0 + 12 Combine like terms: 0 + 12 = 12 -12a + a2 = 12 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 = 12 + 36 Reorder the terms: 36 + -12a + a2 = 12 + 36 Combine like terms: 12 + 36 = 48 36 + -12a + a2 = 48 Factor a perfect square on the left side: (a + -6)(a + -6) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (a + -6) equal to 6.92820323 and -6.92820323.Subproblem 1
a + -6 = 6.92820323 Simplifying a + -6 = 6.92820323 Reorder the terms: -6 + a = 6.92820323 Solving -6 + a = 6.92820323 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 = 6.92820323 + 6 Combine like terms: -6 + 6 = 0 0 + a = 6.92820323 + 6 a = 6.92820323 + 6 Combine like terms: 6.92820323 + 6 = 12.92820323 a = 12.92820323 Simplifying a = 12.92820323Subproblem 2
a + -6 = -6.92820323 Simplifying a + -6 = -6.92820323 Reorder the terms: -6 + a = -6.92820323 Solving -6 + a = -6.92820323 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 = -6.92820323 + 6 Combine like terms: -6 + 6 = 0 0 + a = -6.92820323 + 6 a = -6.92820323 + 6 Combine like terms: -6.92820323 + 6 = -0.92820323 a = -0.92820323 Simplifying a = -0.92820323Solution
The solution to the problem is based on the solutions from the subproblems. a = {12.92820323, -0.92820323}
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