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Simplifying a2 + -24a + 96 = 0 Reorder the terms: 96 + -24a + a2 = 0 Solving 96 + -24a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + -24a + -96 + a2 = 0 + -96 Reorder the terms: 96 + -96 + -24a + a2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -24a + a2 = 0 + -96 -24a + a2 = 0 + -96 Combine like terms: 0 + -96 = -96 -24a + a2 = -96 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 = -96 + 144 Reorder the terms: 144 + -24a + a2 = -96 + 144 Combine like terms: -96 + 144 = 48 144 + -24a + a2 = 48 Factor a perfect square on the left side: (a + -12)(a + -12) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (a + -12) equal to 6.92820323 and -6.92820323.Subproblem 1
a + -12 = 6.92820323 Simplifying a + -12 = 6.92820323 Reorder the terms: -12 + a = 6.92820323 Solving -12 + a = 6.92820323 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 = 6.92820323 + 12 Combine like terms: -12 + 12 = 0 0 + a = 6.92820323 + 12 a = 6.92820323 + 12 Combine like terms: 6.92820323 + 12 = 18.92820323 a = 18.92820323 Simplifying a = 18.92820323Subproblem 2
a + -12 = -6.92820323 Simplifying a + -12 = -6.92820323 Reorder the terms: -12 + a = -6.92820323 Solving -12 + a = -6.92820323 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 = -6.92820323 + 12 Combine like terms: -12 + 12 = 0 0 + a = -6.92820323 + 12 a = -6.92820323 + 12 Combine like terms: -6.92820323 + 12 = 5.07179677 a = 5.07179677 Simplifying a = 5.07179677Solution
The solution to the problem is based on the solutions from the subproblems. a = {18.92820323, 5.07179677}
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