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Simplifying a(11 + -1a) = 26 (11 * a + -1a * a) = 26 (11a + -1a2) = 26 Solving 11a + -1a2 = 26 Solving for variable 'a'. Reorder the terms: -26 + 11a + -1a2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 11a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 26 + -11a + a2 = 0 Move the constant term to the right: Add '-26' to each side of the equation. 26 + -11a + -26 + a2 = 0 + -26 Reorder the terms: 26 + -26 + -11a + a2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -11a + a2 = 0 + -26 -11a + a2 = 0 + -26 Combine like terms: 0 + -26 = -26 -11a + a2 = -26 The a term is -11a. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11a + 30.25 + a2 = -26 + 30.25 Reorder the terms: 30.25 + -11a + a2 = -26 + 30.25 Combine like terms: -26 + 30.25 = 4.25 30.25 + -11a + a2 = 4.25 Factor a perfect square on the left side: (a + -5.5)(a + -5.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (a + -5.5) equal to 2.061552813 and -2.061552813.Subproblem 1
a + -5.5 = 2.061552813 Simplifying a + -5.5 = 2.061552813 Reorder the terms: -5.5 + a = 2.061552813 Solving -5.5 + a = 2.061552813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = 2.061552813 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = 2.061552813 + 5.5 a = 2.061552813 + 5.5 Combine like terms: 2.061552813 + 5.5 = 7.561552813 a = 7.561552813 Simplifying a = 7.561552813Subproblem 2
a + -5.5 = -2.061552813 Simplifying a + -5.5 = -2.061552813 Reorder the terms: -5.5 + a = -2.061552813 Solving -5.5 + a = -2.061552813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = -2.061552813 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = -2.061552813 + 5.5 a = -2.061552813 + 5.5 Combine like terms: -2.061552813 + 5.5 = 3.438447187 a = 3.438447187 Simplifying a = 3.438447187Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.561552813, 3.438447187}
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