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Simplifying 2a2 + 29a + -7 = 0 Reorder the terms: -7 + 29a + 2a2 = 0 Solving -7 + 29a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 14.5a + a2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 14.5a + 3.5 + a2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 14.5a + a2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 14.5a + a2 = 0 + 3.5 14.5a + a2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 14.5a + a2 = 3.5 The a term is 14.5a. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5a + 52.5625 + a2 = 3.5 + 52.5625 Reorder the terms: 52.5625 + 14.5a + a2 = 3.5 + 52.5625 Combine like terms: 3.5 + 52.5625 = 56.0625 52.5625 + 14.5a + a2 = 56.0625 Factor a perfect square on the left side: (a + 7.25)(a + 7.25) = 56.0625 Calculate the square root of the right side: 7.487489566 Break this problem into two subproblems by setting (a + 7.25) equal to 7.487489566 and -7.487489566.Subproblem 1
a + 7.25 = 7.487489566 Simplifying a + 7.25 = 7.487489566 Reorder the terms: 7.25 + a = 7.487489566 Solving 7.25 + a = 7.487489566 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + a = 7.487489566 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + a = 7.487489566 + -7.25 a = 7.487489566 + -7.25 Combine like terms: 7.487489566 + -7.25 = 0.237489566 a = 0.237489566 Simplifying a = 0.237489566Subproblem 2
a + 7.25 = -7.487489566 Simplifying a + 7.25 = -7.487489566 Reorder the terms: 7.25 + a = -7.487489566 Solving 7.25 + a = -7.487489566 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + a = -7.487489566 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + a = -7.487489566 + -7.25 a = -7.487489566 + -7.25 Combine like terms: -7.487489566 + -7.25 = -14.737489566 a = -14.737489566 Simplifying a = -14.737489566Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.237489566, -14.737489566}
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