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Simplifying a2 + -16a + -27 = 0 Reorder the terms: -27 + -16a + a2 = 0 Solving -27 + -16a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -16a + 27 + a2 = 0 + 27 Reorder the terms: -27 + 27 + -16a + a2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -16a + a2 = 0 + 27 -16a + a2 = 0 + 27 Combine like terms: 0 + 27 = 27 -16a + a2 = 27 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 = 27 + 64 Reorder the terms: 64 + -16a + a2 = 27 + 64 Combine like terms: 27 + 64 = 91 64 + -16a + a2 = 91 Factor a perfect square on the left side: (a + -8)(a + -8) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (a + -8) equal to 9.539392014 and -9.539392014.Subproblem 1
a + -8 = 9.539392014 Simplifying a + -8 = 9.539392014 Reorder the terms: -8 + a = 9.539392014 Solving -8 + a = 9.539392014 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 = 9.539392014 + 8 Combine like terms: -8 + 8 = 0 0 + a = 9.539392014 + 8 a = 9.539392014 + 8 Combine like terms: 9.539392014 + 8 = 17.539392014 a = 17.539392014 Simplifying a = 17.539392014Subproblem 2
a + -8 = -9.539392014 Simplifying a + -8 = -9.539392014 Reorder the terms: -8 + a = -9.539392014 Solving -8 + a = -9.539392014 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 = -9.539392014 + 8 Combine like terms: -8 + 8 = 0 0 + a = -9.539392014 + 8 a = -9.539392014 + 8 Combine like terms: -9.539392014 + 8 = -1.539392014 a = -1.539392014 Simplifying a = -1.539392014Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.539392014, -1.539392014}
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