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Simplifying 5a2 + 49a + 49 = 0 Reorder the terms: 49 + 49a + 5a2 = 0 Solving 49 + 49a + 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'. 9.8 + 9.8a + a2 = 0 Move the constant term to the right: Add '-9.8' to each side of the equation. 9.8 + 9.8a + -9.8 + a2 = 0 + -9.8 Reorder the terms: 9.8 + -9.8 + 9.8a + a2 = 0 + -9.8 Combine like terms: 9.8 + -9.8 = 0.0 0.0 + 9.8a + a2 = 0 + -9.8 9.8a + a2 = 0 + -9.8 Combine like terms: 0 + -9.8 = -9.8 9.8a + a2 = -9.8 The a term is 9.8a. Take half its coefficient (4.9). Square it (24.01) and add it to both sides. Add '24.01' to each side of the equation. 9.8a + 24.01 + a2 = -9.8 + 24.01 Reorder the terms: 24.01 + 9.8a + a2 = -9.8 + 24.01 Combine like terms: -9.8 + 24.01 = 14.21 24.01 + 9.8a + a2 = 14.21 Factor a perfect square on the left side: (a + 4.9)(a + 4.9) = 14.21 Calculate the square root of the right side: 3.769615365 Break this problem into two subproblems by setting (a + 4.9) equal to 3.769615365 and -3.769615365.Subproblem 1
a + 4.9 = 3.769615365 Simplifying a + 4.9 = 3.769615365 Reorder the terms: 4.9 + a = 3.769615365 Solving 4.9 + a = 3.769615365 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.9' to each side of the equation. 4.9 + -4.9 + a = 3.769615365 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + a = 3.769615365 + -4.9 a = 3.769615365 + -4.9 Combine like terms: 3.769615365 + -4.9 = -1.130384635 a = -1.130384635 Simplifying a = -1.130384635Subproblem 2
a + 4.9 = -3.769615365 Simplifying a + 4.9 = -3.769615365 Reorder the terms: 4.9 + a = -3.769615365 Solving 4.9 + a = -3.769615365 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.9' to each side of the equation. 4.9 + -4.9 + a = -3.769615365 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + a = -3.769615365 + -4.9 a = -3.769615365 + -4.9 Combine like terms: -3.769615365 + -4.9 = -8.669615365 a = -8.669615365 Simplifying a = -8.669615365Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.130384635, -8.669615365}
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