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Simplifying a2 + 12a + 36 = 43 Reorder the terms: 36 + 12a + a2 = 43 Solving 36 + 12a + a2 = 43 Solving for variable 'a'. Reorder the terms: 36 + -43 + 12a + a2 = 43 + -43 Combine like terms: 36 + -43 = -7 -7 + 12a + a2 = 43 + -43 Combine like terms: 43 + -43 = 0 -7 + 12a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 12a + 7 + a2 = 0 + 7 Reorder the terms: -7 + 7 + 12a + a2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 12a + a2 = 0 + 7 12a + a2 = 0 + 7 Combine like terms: 0 + 7 = 7 12a + a2 = 7 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 = 7 + 36 Reorder the terms: 36 + 12a + a2 = 7 + 36 Combine like terms: 7 + 36 = 43 36 + 12a + a2 = 43 Factor a perfect square on the left side: (a + 6)(a + 6) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (a + 6) equal to 6.557438524 and -6.557438524.Subproblem 1
a + 6 = 6.557438524 Simplifying a + 6 = 6.557438524 Reorder the terms: 6 + a = 6.557438524 Solving 6 + a = 6.557438524 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 = 6.557438524 + -6 Combine like terms: 6 + -6 = 0 0 + a = 6.557438524 + -6 a = 6.557438524 + -6 Combine like terms: 6.557438524 + -6 = 0.557438524 a = 0.557438524 Simplifying a = 0.557438524Subproblem 2
a + 6 = -6.557438524 Simplifying a + 6 = -6.557438524 Reorder the terms: 6 + a = -6.557438524 Solving 6 + a = -6.557438524 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 = -6.557438524 + -6 Combine like terms: 6 + -6 = 0 0 + a = -6.557438524 + -6 a = -6.557438524 + -6 Combine like terms: -6.557438524 + -6 = -12.557438524 a = -12.557438524 Simplifying a = -12.557438524Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.557438524, -12.557438524}
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