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Simplifying 5a * 5a + 13a = 6 Reorder the terms for easier multiplication: 5 * 5a * a + 13a = 6 Multiply 5 * 5 25a * a + 13a = 6 Multiply a * a 25a2 + 13a = 6 Reorder the terms: 13a + 25a2 = 6 Solving 13a + 25a2 = 6 Solving for variable 'a'. Reorder the terms: -6 + 13a + 25a2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 13a + 25a2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.24 + 0.52a + a2 = 0 Move the constant term to the right: Add '0.24' to each side of the equation. -0.24 + 0.52a + 0.24 + a2 = 0 + 0.24 Reorder the terms: -0.24 + 0.24 + 0.52a + a2 = 0 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + 0.52a + a2 = 0 + 0.24 0.52a + a2 = 0 + 0.24 Combine like terms: 0 + 0.24 = 0.24 0.52a + a2 = 0.24 The a term is 0.52a. Take half its coefficient (0.26). Square it (0.0676) and add it to both sides. Add '0.0676' to each side of the equation. 0.52a + 0.0676 + a2 = 0.24 + 0.0676 Reorder the terms: 0.0676 + 0.52a + a2 = 0.24 + 0.0676 Combine like terms: 0.24 + 0.0676 = 0.3076 0.0676 + 0.52a + a2 = 0.3076 Factor a perfect square on the left side: (a + 0.26)(a + 0.26) = 0.3076 Calculate the square root of the right side: 0.554616985 Break this problem into two subproblems by setting (a + 0.26) equal to 0.554616985 and -0.554616985.Subproblem 1
a + 0.26 = 0.554616985 Simplifying a + 0.26 = 0.554616985 Reorder the terms: 0.26 + a = 0.554616985 Solving 0.26 + a = 0.554616985 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.26' to each side of the equation. 0.26 + -0.26 + a = 0.554616985 + -0.26 Combine like terms: 0.26 + -0.26 = 0.00 0.00 + a = 0.554616985 + -0.26 a = 0.554616985 + -0.26 Combine like terms: 0.554616985 + -0.26 = 0.294616985 a = 0.294616985 Simplifying a = 0.294616985Subproblem 2
a + 0.26 = -0.554616985 Simplifying a + 0.26 = -0.554616985 Reorder the terms: 0.26 + a = -0.554616985 Solving 0.26 + a = -0.554616985 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.26' to each side of the equation. 0.26 + -0.26 + a = -0.554616985 + -0.26 Combine like terms: 0.26 + -0.26 = 0.00 0.00 + a = -0.554616985 + -0.26 a = -0.554616985 + -0.26 Combine like terms: -0.554616985 + -0.26 = -0.814616985 a = -0.814616985 Simplifying a = -0.814616985Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.294616985, -0.814616985}
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