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Simplifying a(29 + -1a) = 29 (29 * a + -1a * a) = 29 (29a + -1a2) = 29 Solving 29a + -1a2 = 29 Solving for variable 'a'. Reorder the terms: -29 + 29a + -1a2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 29a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 29 + -29a + a2 = 0 Move the constant term to the right: Add '-29' to each side of the equation. 29 + -29a + -29 + a2 = 0 + -29 Reorder the terms: 29 + -29 + -29a + a2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -29a + a2 = 0 + -29 -29a + a2 = 0 + -29 Combine like terms: 0 + -29 = -29 -29a + a2 = -29 The a term is -29a. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29a + 210.25 + a2 = -29 + 210.25 Reorder the terms: 210.25 + -29a + a2 = -29 + 210.25 Combine like terms: -29 + 210.25 = 181.25 210.25 + -29a + a2 = 181.25 Factor a perfect square on the left side: (a + -14.5)(a + -14.5) = 181.25 Calculate the square root of the right side: 13.462912018 Break this problem into two subproblems by setting (a + -14.5) equal to 13.462912018 and -13.462912018.Subproblem 1
a + -14.5 = 13.462912018 Simplifying a + -14.5 = 13.462912018 Reorder the terms: -14.5 + a = 13.462912018 Solving -14.5 + a = 13.462912018 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + a = 13.462912018 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + a = 13.462912018 + 14.5 a = 13.462912018 + 14.5 Combine like terms: 13.462912018 + 14.5 = 27.962912018 a = 27.962912018 Simplifying a = 27.962912018Subproblem 2
a + -14.5 = -13.462912018 Simplifying a + -14.5 = -13.462912018 Reorder the terms: -14.5 + a = -13.462912018 Solving -14.5 + a = -13.462912018 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + a = -13.462912018 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + a = -13.462912018 + 14.5 a = -13.462912018 + 14.5 Combine like terms: -13.462912018 + 14.5 = 1.037087982 a = 1.037087982 Simplifying a = 1.037087982Solution
The solution to the problem is based on the solutions from the subproblems. a = {27.962912018, 1.037087982}
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