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Simplifying a2 + 6a + -48 = -5 Reorder the terms: -48 + 6a + a2 = -5 Solving -48 + 6a + a2 = -5 Solving for variable 'a'. Reorder the terms: -48 + 5 + 6a + a2 = -5 + 5 Combine like terms: -48 + 5 = -43 -43 + 6a + a2 = -5 + 5 Combine like terms: -5 + 5 = 0 -43 + 6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 6a + 43 + a2 = 0 + 43 Reorder the terms: -43 + 43 + 6a + a2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 6a + a2 = 0 + 43 6a + a2 = 0 + 43 Combine like terms: 0 + 43 = 43 6a + a2 = 43 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = 43 + 9 Reorder the terms: 9 + 6a + a2 = 43 + 9 Combine like terms: 43 + 9 = 52 9 + 6a + a2 = 52 Factor a perfect square on the left side: (a + 3)(a + 3) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (a + 3) equal to 7.211102551 and -7.211102551.Subproblem 1
a + 3 = 7.211102551 Simplifying a + 3 = 7.211102551 Reorder the terms: 3 + a = 7.211102551 Solving 3 + a = 7.211102551 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 7.211102551 + -3 Combine like terms: 3 + -3 = 0 0 + a = 7.211102551 + -3 a = 7.211102551 + -3 Combine like terms: 7.211102551 + -3 = 4.211102551 a = 4.211102551 Simplifying a = 4.211102551Subproblem 2
a + 3 = -7.211102551 Simplifying a + 3 = -7.211102551 Reorder the terms: 3 + a = -7.211102551 Solving 3 + a = -7.211102551 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -7.211102551 + -3 Combine like terms: 3 + -3 = 0 0 + a = -7.211102551 + -3 a = -7.211102551 + -3 Combine like terms: -7.211102551 + -3 = -10.211102551 a = -10.211102551 Simplifying a = -10.211102551Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.211102551, -10.211102551}
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