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Simplifying 7a2 + 49a + 60 = 0 Reorder the terms: 60 + 49a + 7a2 = 0 Solving 60 + 49a + 7a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 8.571428571 + 7a + a2 = 0 Move the constant term to the right: Add '-8.571428571' to each side of the equation. 8.571428571 + 7a + -8.571428571 + a2 = 0 + -8.571428571 Reorder the terms: 8.571428571 + -8.571428571 + 7a + a2 = 0 + -8.571428571 Combine like terms: 8.571428571 + -8.571428571 = 0.000000000 0.000000000 + 7a + a2 = 0 + -8.571428571 7a + a2 = 0 + -8.571428571 Combine like terms: 0 + -8.571428571 = -8.571428571 7a + a2 = -8.571428571 The a term is 7a. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7a + 12.25 + a2 = -8.571428571 + 12.25 Reorder the terms: 12.25 + 7a + a2 = -8.571428571 + 12.25 Combine like terms: -8.571428571 + 12.25 = 3.678571429 12.25 + 7a + a2 = 3.678571429 Factor a perfect square on the left side: (a + 3.5)(a + 3.5) = 3.678571429 Calculate the square root of the right side: 1.917960226 Break this problem into two subproblems by setting (a + 3.5) equal to 1.917960226 and -1.917960226.Subproblem 1
a + 3.5 = 1.917960226 Simplifying a + 3.5 = 1.917960226 Reorder the terms: 3.5 + a = 1.917960226 Solving 3.5 + a = 1.917960226 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = 1.917960226 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = 1.917960226 + -3.5 a = 1.917960226 + -3.5 Combine like terms: 1.917960226 + -3.5 = -1.582039774 a = -1.582039774 Simplifying a = -1.582039774Subproblem 2
a + 3.5 = -1.917960226 Simplifying a + 3.5 = -1.917960226 Reorder the terms: 3.5 + a = -1.917960226 Solving 3.5 + a = -1.917960226 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = -1.917960226 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = -1.917960226 + -3.5 a = -1.917960226 + -3.5 Combine like terms: -1.917960226 + -3.5 = -5.417960226 a = -5.417960226 Simplifying a = -5.417960226Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.582039774, -5.417960226}
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