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Simplifying 5a2 + 29a + 10 = 0 Reorder the terms: 10 + 29a + 5a2 = 0 Solving 10 + 29a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 5.8a + a2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 5.8a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + 5.8a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5.8a + a2 = 0 + -2 5.8a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 5.8a + a2 = -2 The a term is 5.8a. Take half its coefficient (2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. 5.8a + 8.41 + a2 = -2 + 8.41 Reorder the terms: 8.41 + 5.8a + a2 = -2 + 8.41 Combine like terms: -2 + 8.41 = 6.41 8.41 + 5.8a + a2 = 6.41 Factor a perfect square on the left side: (a + 2.9)(a + 2.9) = 6.41 Calculate the square root of the right side: 2.53179778 Break this problem into two subproblems by setting (a + 2.9) equal to 2.53179778 and -2.53179778.Subproblem 1
a + 2.9 = 2.53179778 Simplifying a + 2.9 = 2.53179778 Reorder the terms: 2.9 + a = 2.53179778 Solving 2.9 + a = 2.53179778 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + a = 2.53179778 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + a = 2.53179778 + -2.9 a = 2.53179778 + -2.9 Combine like terms: 2.53179778 + -2.9 = -0.36820222 a = -0.36820222 Simplifying a = -0.36820222Subproblem 2
a + 2.9 = -2.53179778 Simplifying a + 2.9 = -2.53179778 Reorder the terms: 2.9 + a = -2.53179778 Solving 2.9 + a = -2.53179778 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + a = -2.53179778 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + a = -2.53179778 + -2.9 a = -2.53179778 + -2.9 Combine like terms: -2.53179778 + -2.9 = -5.43179778 a = -5.43179778 Simplifying a = -5.43179778Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.36820222, -5.43179778}
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