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Simplifying 2.798a(9a + 2) = 6 Reorder the terms: 2.798a(2 + 9a) = 6 (2 * 2.798a + 9a * 2.798a) = 6 (5.596a + 25.182a2) = 6 Solving 5.596a + 25.182a2 = 6 Solving for variable 'a'. Reorder the terms: -6 + 5.596a + 25.182a2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 5.596a + 25.182a2 = 0 Begin completing the square. Divide all terms by 25.182 the coefficient of the squared term: Divide each side by '25.182'. -0.2382654277 + 0.2222222222a + a2 = 0 Move the constant term to the right: Add '0.2382654277' to each side of the equation. -0.2382654277 + 0.2222222222a + 0.2382654277 + a2 = 0 + 0.2382654277 Reorder the terms: -0.2382654277 + 0.2382654277 + 0.2222222222a + a2 = 0 + 0.2382654277 Combine like terms: -0.2382654277 + 0.2382654277 = 0.0000000000 0.0000000000 + 0.2222222222a + a2 = 0 + 0.2382654277 0.2222222222a + a2 = 0 + 0.2382654277 Combine like terms: 0 + 0.2382654277 = 0.2382654277 0.2222222222a + a2 = 0.2382654277 The a term is 0.2222222222a. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222a + 0.01234567901 + a2 = 0.2382654277 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222a + a2 = 0.2382654277 + 0.01234567901 Combine like terms: 0.2382654277 + 0.01234567901 = 0.25061110671 0.01234567901 + 0.2222222222a + a2 = 0.25061110671 Factor a perfect square on the left side: (a + 0.1111111111)(a + 0.1111111111) = 0.25061110671 Calculate the square root of the right side: 0.500610734 Break this problem into two subproblems by setting (a + 0.1111111111) equal to 0.500610734 and -0.500610734.Subproblem 1
a + 0.1111111111 = 0.500610734 Simplifying a + 0.1111111111 = 0.500610734 Reorder the terms: 0.1111111111 + a = 0.500610734 Solving 0.1111111111 + a = 0.500610734 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + a = 0.500610734 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + a = 0.500610734 + -0.1111111111 a = 0.500610734 + -0.1111111111 Combine like terms: 0.500610734 + -0.1111111111 = 0.3894996229 a = 0.3894996229 Simplifying a = 0.3894996229Subproblem 2
a + 0.1111111111 = -0.500610734 Simplifying a + 0.1111111111 = -0.500610734 Reorder the terms: 0.1111111111 + a = -0.500610734 Solving 0.1111111111 + a = -0.500610734 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + a = -0.500610734 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + a = -0.500610734 + -0.1111111111 a = -0.500610734 + -0.1111111111 Combine like terms: -0.500610734 + -0.1111111111 = -0.6117218451 a = -0.6117218451 Simplifying a = -0.6117218451Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.3894996229, -0.6117218451}
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