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Simplifying a2 + -12a + -72 = 0 Reorder the terms: -72 + -12a + a2 = 0 Solving -72 + -12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -12a + 72 + a2 = 0 + 72 Reorder the terms: -72 + 72 + -12a + a2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -12a + a2 = 0 + 72 -12a + a2 = 0 + 72 Combine like terms: 0 + 72 = 72 -12a + a2 = 72 The a term is -12a. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a + 36 + a2 = 72 + 36 Reorder the terms: 36 + -12a + a2 = 72 + 36 Combine like terms: 72 + 36 = 108 36 + -12a + a2 = 108 Factor a perfect square on the left side: (a + -6)(a + -6) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (a + -6) equal to 10.392304845 and -10.392304845.Subproblem 1
a + -6 = 10.392304845 Simplifying a + -6 = 10.392304845 Reorder the terms: -6 + a = 10.392304845 Solving -6 + a = 10.392304845 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 10.392304845 + 6 Combine like terms: -6 + 6 = 0 0 + a = 10.392304845 + 6 a = 10.392304845 + 6 Combine like terms: 10.392304845 + 6 = 16.392304845 a = 16.392304845 Simplifying a = 16.392304845Subproblem 2
a + -6 = -10.392304845 Simplifying a + -6 = -10.392304845 Reorder the terms: -6 + a = -10.392304845 Solving -6 + a = -10.392304845 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = -10.392304845 + 6 Combine like terms: -6 + 6 = 0 0 + a = -10.392304845 + 6 a = -10.392304845 + 6 Combine like terms: -10.392304845 + 6 = -4.392304845 a = -4.392304845 Simplifying a = -4.392304845Solution
The solution to the problem is based on the solutions from the subproblems. a = {16.392304845, -4.392304845}
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