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Simplifying a2 + -24a + 36 = 0 Reorder the terms: 36 + -24a + a2 = 0 Solving 36 + -24a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -24a + -36 + a2 = 0 + -36 Reorder the terms: 36 + -36 + -24a + a2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -24a + a2 = 0 + -36 -24a + a2 = 0 + -36 Combine like terms: 0 + -36 = -36 -24a + a2 = -36 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 = -36 + 144 Reorder the terms: 144 + -24a + a2 = -36 + 144 Combine like terms: -36 + 144 = 108 144 + -24a + a2 = 108 Factor a perfect square on the left side: (a + -12)(a + -12) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (a + -12) equal to 10.392304845 and -10.392304845.Subproblem 1
a + -12 = 10.392304845 Simplifying a + -12 = 10.392304845 Reorder the terms: -12 + a = 10.392304845 Solving -12 + a = 10.392304845 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 = 10.392304845 + 12 Combine like terms: -12 + 12 = 0 0 + a = 10.392304845 + 12 a = 10.392304845 + 12 Combine like terms: 10.392304845 + 12 = 22.392304845 a = 22.392304845 Simplifying a = 22.392304845Subproblem 2
a + -12 = -10.392304845 Simplifying a + -12 = -10.392304845 Reorder the terms: -12 + a = -10.392304845 Solving -12 + a = -10.392304845 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 = -10.392304845 + 12 Combine like terms: -12 + 12 = 0 0 + a = -10.392304845 + 12 a = -10.392304845 + 12 Combine like terms: -10.392304845 + 12 = 1.607695155 a = 1.607695155 Simplifying a = 1.607695155Solution
The solution to the problem is based on the solutions from the subproblems. a = {22.392304845, 1.607695155}
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