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Simplifying 19a2 + 10a = -11a + 4 Reorder the terms: 10a + 19a2 = -11a + 4 Reorder the terms: 10a + 19a2 = 4 + -11a Solving 10a + 19a2 = 4 + -11a Solving for variable 'a'. Reorder the terms: -4 + 10a + 11a + 19a2 = 4 + -11a + -4 + 11a Combine like terms: 10a + 11a = 21a -4 + 21a + 19a2 = 4 + -11a + -4 + 11a Reorder the terms: -4 + 21a + 19a2 = 4 + -4 + -11a + 11a Combine like terms: 4 + -4 = 0 -4 + 21a + 19a2 = 0 + -11a + 11a -4 + 21a + 19a2 = -11a + 11a Combine like terms: -11a + 11a = 0 -4 + 21a + 19a2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.2105263158 + 1.105263158a + a2 = 0 Move the constant term to the right: Add '0.2105263158' to each side of the equation. -0.2105263158 + 1.105263158a + 0.2105263158 + a2 = 0 + 0.2105263158 Reorder the terms: -0.2105263158 + 0.2105263158 + 1.105263158a + a2 = 0 + 0.2105263158 Combine like terms: -0.2105263158 + 0.2105263158 = 0.0000000000 0.0000000000 + 1.105263158a + a2 = 0 + 0.2105263158 1.105263158a + a2 = 0 + 0.2105263158 Combine like terms: 0 + 0.2105263158 = 0.2105263158 1.105263158a + a2 = 0.2105263158 The a term is 1.105263158a. Take half its coefficient (0.552631579). Square it (0.3054016621) and add it to both sides. Add '0.3054016621' to each side of the equation. 1.105263158a + 0.3054016621 + a2 = 0.2105263158 + 0.3054016621 Reorder the terms: 0.3054016621 + 1.105263158a + a2 = 0.2105263158 + 0.3054016621 Combine like terms: 0.2105263158 + 0.3054016621 = 0.5159279779 0.3054016621 + 1.105263158a + a2 = 0.5159279779 Factor a perfect square on the left side: (a + 0.552631579)(a + 0.552631579) = 0.5159279779 Calculate the square root of the right side: 0.718281267 Break this problem into two subproblems by setting (a + 0.552631579) equal to 0.718281267 and -0.718281267.Subproblem 1
a + 0.552631579 = 0.718281267 Simplifying a + 0.552631579 = 0.718281267 Reorder the terms: 0.552631579 + a = 0.718281267 Solving 0.552631579 + a = 0.718281267 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.552631579' to each side of the equation. 0.552631579 + -0.552631579 + a = 0.718281267 + -0.552631579 Combine like terms: 0.552631579 + -0.552631579 = 0.000000000 0.000000000 + a = 0.718281267 + -0.552631579 a = 0.718281267 + -0.552631579 Combine like terms: 0.718281267 + -0.552631579 = 0.165649688 a = 0.165649688 Simplifying a = 0.165649688Subproblem 2
a + 0.552631579 = -0.718281267 Simplifying a + 0.552631579 = -0.718281267 Reorder the terms: 0.552631579 + a = -0.718281267 Solving 0.552631579 + a = -0.718281267 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.552631579' to each side of the equation. 0.552631579 + -0.552631579 + a = -0.718281267 + -0.552631579 Combine like terms: 0.552631579 + -0.552631579 = 0.000000000 0.000000000 + a = -0.718281267 + -0.552631579 a = -0.718281267 + -0.552631579 Combine like terms: -0.718281267 + -0.552631579 = -1.270912846 a = -1.270912846 Simplifying a = -1.270912846Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.165649688, -1.270912846}
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