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Simplifying a2 + -4a = 16 Reorder the terms: -4a + a2 = 16 Solving -4a + a2 = 16 Solving for variable 'a'. Reorder the terms: -16 + -4a + a2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -4a + 16 + a2 = 0 + 16 Reorder the terms: -16 + 16 + -4a + a2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -4a + a2 = 0 + 16 -4a + a2 = 0 + 16 Combine like terms: 0 + 16 = 16 -4a + a2 = 16 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 16 + 4 Reorder the terms: 4 + -4a + a2 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + -4a + a2 = 20 Factor a perfect square on the left side: (a + -2)(a + -2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (a + -2) equal to 4.472135955 and -4.472135955.Subproblem 1
a + -2 = 4.472135955 Simplifying a + -2 = 4.472135955 Reorder the terms: -2 + a = 4.472135955 Solving -2 + a = 4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + a = 4.472135955 + 2 a = 4.472135955 + 2 Combine like terms: 4.472135955 + 2 = 6.472135955 a = 6.472135955 Simplifying a = 6.472135955Subproblem 2
a + -2 = -4.472135955 Simplifying a + -2 = -4.472135955 Reorder the terms: -2 + a = -4.472135955 Solving -2 + a = -4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + a = -4.472135955 + 2 a = -4.472135955 + 2 Combine like terms: -4.472135955 + 2 = -2.472135955 a = -2.472135955 Simplifying a = -2.472135955Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.472135955, -2.472135955}
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