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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 = 24 36 + 12a + a2 = 24 Factor a perfect square on the left side: (a + 6)(a + 6) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (a + 6) equal to 4.898979486 and -4.898979486.Subproblem 1
a + 6 = 4.898979486 Simplifying a + 6 = 4.898979486 Reorder the terms: 6 + a = 4.898979486 Solving 6 + a = 4.898979486 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 = 4.898979486 + -6 Combine like terms: 6 + -6 = 0 0 + a = 4.898979486 + -6 a = 4.898979486 + -6 Combine like terms: 4.898979486 + -6 = -1.101020514 a = -1.101020514 Simplifying a = -1.101020514Subproblem 2
a + 6 = -4.898979486 Simplifying a + 6 = -4.898979486 Reorder the terms: 6 + a = -4.898979486 Solving 6 + a = -4.898979486 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 = -4.898979486 + -6 Combine like terms: 6 + -6 = 0 0 + a = -4.898979486 + -6 a = -4.898979486 + -6 Combine like terms: -4.898979486 + -6 = -10.898979486 a = -10.898979486 Simplifying a = -10.898979486Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.101020514, -10.898979486}
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