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Simplifying a2 + -16a + -60 = 0 Reorder the terms: -60 + -16a + a2 = 0 Solving -60 + -16a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -16a + 60 + a2 = 0 + 60 Reorder the terms: -60 + 60 + -16a + a2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -16a + a2 = 0 + 60 -16a + a2 = 0 + 60 Combine like terms: 0 + 60 = 60 -16a + a2 = 60 The a term is -16a. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16a + 64 + a2 = 60 + 64 Reorder the terms: 64 + -16a + a2 = 60 + 64 Combine like terms: 60 + 64 = 124 64 + -16a + a2 = 124 Factor a perfect square on the left side: (a + -8)(a + -8) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (a + -8) equal to 11.135528726 and -11.135528726.Subproblem 1
a + -8 = 11.135528726 Simplifying a + -8 = 11.135528726 Reorder the terms: -8 + a = 11.135528726 Solving -8 + a = 11.135528726 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = 11.135528726 + 8 Combine like terms: -8 + 8 = 0 0 + a = 11.135528726 + 8 a = 11.135528726 + 8 Combine like terms: 11.135528726 + 8 = 19.135528726 a = 19.135528726 Simplifying a = 19.135528726Subproblem 2
a + -8 = -11.135528726 Simplifying a + -8 = -11.135528726 Reorder the terms: -8 + a = -11.135528726 Solving -8 + a = -11.135528726 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a = -11.135528726 + 8 Combine like terms: -8 + 8 = 0 0 + a = -11.135528726 + 8 a = -11.135528726 + 8 Combine like terms: -11.135528726 + 8 = -3.135528726 a = -3.135528726 Simplifying a = -3.135528726Solution
The solution to the problem is based on the solutions from the subproblems. a = {19.135528726, -3.135528726}
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