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Simplifying -2a(a + 6) = -22 Reorder the terms: -2a(6 + a) = -22 (6 * -2a + a * -2a) = -22 (-12a + -2a2) = -22 Solving -12a + -2a2 = -22 Solving for variable 'a'. Reorder the terms: 22 + -12a + -2a2 = -22 + 22 Combine like terms: -22 + 22 = 0 22 + -12a + -2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -6a + -1a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -6a + -1a2)' equal to zero and attempt to solve: Simplifying 11 + -6a + -1a2 = 0 Solving 11 + -6a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + 6a + a2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 6a + 11 + a2 = 0 + 11 Reorder the terms: -11 + 11 + 6a + a2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6a + a2 = 0 + 11 6a + a2 = 0 + 11 Combine like terms: 0 + 11 = 11 6a + a2 = 11 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = 11 + 9 Reorder the terms: 9 + 6a + a2 = 11 + 9 Combine like terms: 11 + 9 = 20 9 + 6a + a2 = 20 Factor a perfect square on the left side: (a + 3)(a + 3) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (a + 3) equal to 4.472135955 and -4.472135955.Subproblem 1
a + 3 = 4.472135955 Simplifying a + 3 = 4.472135955 Reorder the terms: 3 + a = 4.472135955 Solving 3 + a = 4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + a = 4.472135955 + -3 a = 4.472135955 + -3 Combine like terms: 4.472135955 + -3 = 1.472135955 a = 1.472135955 Simplifying a = 1.472135955Subproblem 2
a + 3 = -4.472135955 Simplifying a + 3 = -4.472135955 Reorder the terms: 3 + a = -4.472135955 Solving 3 + a = -4.472135955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -4.472135955 + -3 Combine like terms: 3 + -3 = 0 0 + a = -4.472135955 + -3 a = -4.472135955 + -3 Combine like terms: -4.472135955 + -3 = -7.472135955 a = -7.472135955 Simplifying a = -7.472135955Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.472135955, -7.472135955}Solution
a = {1.472135955, -7.472135955}
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