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Simplifying -1a2 + 8a = -4 Reorder the terms: 8a + -1a2 = -4 Solving 8a + -1a2 = -4 Solving for variable 'a'. Reorder the terms: 4 + 8a + -1a2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 8a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -8a + a2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -8a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + -8a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8a + a2 = 0 + 4 -8a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 -8a + a2 = 4 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = 4 + 16 Reorder the terms: 16 + -8a + a2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + -8a + a2 = 20 Factor a perfect square on the left side: (a + -4)(a + -4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (a + -4) equal to 4.472135955 and -4.472135955.Subproblem 1
a + -4 = 4.472135955 Simplifying a + -4 = 4.472135955 Reorder the terms: -4 + a = 4.472135955 Solving -4 + a = 4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + a = 4.472135955 + 4 a = 4.472135955 + 4 Combine like terms: 4.472135955 + 4 = 8.472135955 a = 8.472135955 Simplifying a = 8.472135955Subproblem 2
a + -4 = -4.472135955 Simplifying a + -4 = -4.472135955 Reorder the terms: -4 + a = -4.472135955 Solving -4 + a = -4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + a = -4.472135955 + 4 a = -4.472135955 + 4 Combine like terms: -4.472135955 + 4 = -0.472135955 a = -0.472135955 Simplifying a = -0.472135955Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.472135955, -0.472135955}
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