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Simplifying a2 + 24a + -48 = 0 Reorder the terms: -48 + 24a + a2 = 0 Solving -48 + 24a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 24a + 48 + a2 = 0 + 48 Reorder the terms: -48 + 48 + 24a + a2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 24a + a2 = 0 + 48 24a + a2 = 0 + 48 Combine like terms: 0 + 48 = 48 24a + a2 = 48 The a term is 24a. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24a + 144 + a2 = 48 + 144 Reorder the terms: 144 + 24a + a2 = 48 + 144 Combine like terms: 48 + 144 = 192 144 + 24a + a2 = 192 Factor a perfect square on the left side: (a + 12)(a + 12) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (a + 12) equal to 13.856406461 and -13.856406461.Subproblem 1
a + 12 = 13.856406461 Simplifying a + 12 = 13.856406461 Reorder the terms: 12 + a = 13.856406461 Solving 12 + a = 13.856406461 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + a = 13.856406461 + -12 Combine like terms: 12 + -12 = 0 0 + a = 13.856406461 + -12 a = 13.856406461 + -12 Combine like terms: 13.856406461 + -12 = 1.856406461 a = 1.856406461 Simplifying a = 1.856406461Subproblem 2
a + 12 = -13.856406461 Simplifying a + 12 = -13.856406461 Reorder the terms: 12 + a = -13.856406461 Solving 12 + a = -13.856406461 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + a = -13.856406461 + -12 Combine like terms: 12 + -12 = 0 0 + a = -13.856406461 + -12 a = -13.856406461 + -12 Combine like terms: -13.856406461 + -12 = -25.856406461 a = -25.856406461 Simplifying a = -25.856406461Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.856406461, -25.856406461}
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