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Simplifying a2 = 24(a + -1) Reorder the terms: a2 = 24(-1 + a) a2 = (-1 * 24 + a * 24) a2 = (-24 + 24a) Solving a2 = -24 + 24a Solving for variable 'a'. Reorder the terms: 24 + -24a + a2 = -24 + 24a + 24 + -24a Reorder the terms: 24 + -24a + a2 = -24 + 24 + 24a + -24a Combine like terms: -24 + 24 = 0 24 + -24a + a2 = 0 + 24a + -24a 24 + -24a + a2 = 24a + -24a Combine like terms: 24a + -24a = 0 24 + -24a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -24a + -24 + a2 = 0 + -24 Reorder the terms: 24 + -24 + -24a + a2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -24a + a2 = 0 + -24 -24a + a2 = 0 + -24 Combine like terms: 0 + -24 = -24 -24a + a2 = -24 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 = -24 + 144 Reorder the terms: 144 + -24a + a2 = -24 + 144 Combine like terms: -24 + 144 = 120 144 + -24a + a2 = 120 Factor a perfect square on the left side: (a + -12)(a + -12) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (a + -12) equal to 10.95445115 and -10.95445115.Subproblem 1
a + -12 = 10.95445115 Simplifying a + -12 = 10.95445115 Reorder the terms: -12 + a = 10.95445115 Solving -12 + a = 10.95445115 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 = 10.95445115 + 12 Combine like terms: -12 + 12 = 0 0 + a = 10.95445115 + 12 a = 10.95445115 + 12 Combine like terms: 10.95445115 + 12 = 22.95445115 a = 22.95445115 Simplifying a = 22.95445115Subproblem 2
a + -12 = -10.95445115 Simplifying a + -12 = -10.95445115 Reorder the terms: -12 + a = -10.95445115 Solving -12 + a = -10.95445115 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 = -10.95445115 + 12 Combine like terms: -12 + 12 = 0 0 + a = -10.95445115 + 12 a = -10.95445115 + 12 Combine like terms: -10.95445115 + 12 = 1.04554885 a = 1.04554885 Simplifying a = 1.04554885Solution
The solution to the problem is based on the solutions from the subproblems. a = {22.95445115, 1.04554885}
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