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Simplifying 11a(a + 20) * 6 = 9300 Reorder the terms: 11a(20 + a) * 6 = 9300 Reorder the terms for easier multiplication: 11 * 6a(20 + a) = 9300 Multiply 11 * 6 66a(20 + a) = 9300 (20 * 66a + a * 66a) = 9300 (1320a + 66a2) = 9300 Solving 1320a + 66a2 = 9300 Solving for variable 'a'. Reorder the terms: -9300 + 1320a + 66a2 = 9300 + -9300 Combine like terms: 9300 + -9300 = 0 -9300 + 1320a + 66a2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-1550 + 220a + 11a2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1550 + 220a + 11a2)' equal to zero and attempt to solve: Simplifying -1550 + 220a + 11a2 = 0 Solving -1550 + 220a + 11a2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -140.9090909 + 20a + a2 = 0 Move the constant term to the right: Add '140.9090909' to each side of the equation. -140.9090909 + 20a + 140.9090909 + a2 = 0 + 140.9090909 Reorder the terms: -140.9090909 + 140.9090909 + 20a + a2 = 0 + 140.9090909 Combine like terms: -140.9090909 + 140.9090909 = 0.0000000 0.0000000 + 20a + a2 = 0 + 140.9090909 20a + a2 = 0 + 140.9090909 Combine like terms: 0 + 140.9090909 = 140.9090909 20a + a2 = 140.9090909 The a term is 20a. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20a + 100 + a2 = 140.9090909 + 100 Reorder the terms: 100 + 20a + a2 = 140.9090909 + 100 Combine like terms: 140.9090909 + 100 = 240.9090909 100 + 20a + a2 = 240.9090909 Factor a perfect square on the left side: (a + 10)(a + 10) = 240.9090909 Calculate the square root of the right side: 15.521246435 Break this problem into two subproblems by setting (a + 10) equal to 15.521246435 and -15.521246435.Subproblem 1
a + 10 = 15.521246435 Simplifying a + 10 = 15.521246435 Reorder the terms: 10 + a = 15.521246435 Solving 10 + a = 15.521246435 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = 15.521246435 + -10 Combine like terms: 10 + -10 = 0 0 + a = 15.521246435 + -10 a = 15.521246435 + -10 Combine like terms: 15.521246435 + -10 = 5.521246435 a = 5.521246435 Simplifying a = 5.521246435Subproblem 2
a + 10 = -15.521246435 Simplifying a + 10 = -15.521246435 Reorder the terms: 10 + a = -15.521246435 Solving 10 + a = -15.521246435 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = -15.521246435 + -10 Combine like terms: 10 + -10 = 0 0 + a = -15.521246435 + -10 a = -15.521246435 + -10 Combine like terms: -15.521246435 + -10 = -25.521246435 a = -25.521246435 Simplifying a = -25.521246435Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.521246435, -25.521246435}Solution
a = {5.521246435, -25.521246435}
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