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Simplifying a2 + 14a + -60 = 0 Reorder the terms: -60 + 14a + a2 = 0 Solving -60 + 14a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 14a + 60 + a2 = 0 + 60 Reorder the terms: -60 + 60 + 14a + a2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 14a + a2 = 0 + 60 14a + a2 = 0 + 60 Combine like terms: 0 + 60 = 60 14a + a2 = 60 The a term is 14a. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14a + 49 + a2 = 60 + 49 Reorder the terms: 49 + 14a + a2 = 60 + 49 Combine like terms: 60 + 49 = 109 49 + 14a + a2 = 109 Factor a perfect square on the left side: (a + 7)(a + 7) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (a + 7) equal to 10.440306509 and -10.440306509.Subproblem 1
a + 7 = 10.440306509 Simplifying a + 7 = 10.440306509 Reorder the terms: 7 + a = 10.440306509 Solving 7 + a = 10.440306509 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + a = 10.440306509 + -7 a = 10.440306509 + -7 Combine like terms: 10.440306509 + -7 = 3.440306509 a = 3.440306509 Simplifying a = 3.440306509Subproblem 2
a + 7 = -10.440306509 Simplifying a + 7 = -10.440306509 Reorder the terms: 7 + a = -10.440306509 Solving 7 + a = -10.440306509 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = -10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + a = -10.440306509 + -7 a = -10.440306509 + -7 Combine like terms: -10.440306509 + -7 = -17.440306509 a = -17.440306509 Simplifying a = -17.440306509Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.440306509, -17.440306509}
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