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Simplifying 0 = a2 + -24a + -48 Reorder the terms: 0 = -48 + -24a + a2 Solving 0 = -48 + -24a + a2 Solving for variable 'a'. Combine like terms: 0 + 48 = 48 48 + 24a + -1a2 = -48 + -24a + a2 + 48 + 24a + -1a2 Reorder the terms: 48 + 24a + -1a2 = -48 + 48 + -24a + 24a + a2 + -1a2 Combine like terms: -48 + 48 = 0 48 + 24a + -1a2 = 0 + -24a + 24a + a2 + -1a2 48 + 24a + -1a2 = -24a + 24a + a2 + -1a2 Combine like terms: -24a + 24a = 0 48 + 24a + -1a2 = 0 + a2 + -1a2 48 + 24a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 48 + 24a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + -24a + a2 = 0 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 = 25.856406461 a = 25.856406461 Simplifying a = 25.856406461Subproblem 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 = -1.856406461 a = -1.856406461 Simplifying a = -1.856406461Solution
The solution to the problem is based on the solutions from the subproblems. a = {25.856406461, -1.856406461}
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