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Simplifying 19a2 + -10a + -10 = 0 Reorder the terms: -10 + -10a + 19a2 = 0 Solving -10 + -10a + 19a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.5263157895 + -0.5263157895a + a2 = 0 Move the constant term to the right: Add '0.5263157895' to each side of the equation. -0.5263157895 + -0.5263157895a + 0.5263157895 + a2 = 0 + 0.5263157895 Reorder the terms: -0.5263157895 + 0.5263157895 + -0.5263157895a + a2 = 0 + 0.5263157895 Combine like terms: -0.5263157895 + 0.5263157895 = 0.0000000000 0.0000000000 + -0.5263157895a + a2 = 0 + 0.5263157895 -0.5263157895a + a2 = 0 + 0.5263157895 Combine like terms: 0 + 0.5263157895 = 0.5263157895 -0.5263157895a + a2 = 0.5263157895 The a term is -0.5263157895a. Take half its coefficient (-0.2631578948). Square it (0.06925207760) and add it to both sides. Add '0.06925207760' to each side of the equation. -0.5263157895a + 0.06925207760 + a2 = 0.5263157895 + 0.06925207760 Reorder the terms: 0.06925207760 + -0.5263157895a + a2 = 0.5263157895 + 0.06925207760 Combine like terms: 0.5263157895 + 0.06925207760 = 0.5955678671 0.06925207760 + -0.5263157895a + a2 = 0.5955678671 Factor a perfect square on the left side: (a + -0.2631578948)(a + -0.2631578948) = 0.5955678671 Calculate the square root of the right side: 0.771730437 Break this problem into two subproblems by setting (a + -0.2631578948) equal to 0.771730437 and -0.771730437.Subproblem 1
a + -0.2631578948 = 0.771730437 Simplifying a + -0.2631578948 = 0.771730437 Reorder the terms: -0.2631578948 + a = 0.771730437 Solving -0.2631578948 + a = 0.771730437 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2631578948' to each side of the equation. -0.2631578948 + 0.2631578948 + a = 0.771730437 + 0.2631578948 Combine like terms: -0.2631578948 + 0.2631578948 = 0.0000000000 0.0000000000 + a = 0.771730437 + 0.2631578948 a = 0.771730437 + 0.2631578948 Combine like terms: 0.771730437 + 0.2631578948 = 1.0348883318 a = 1.0348883318 Simplifying a = 1.0348883318Subproblem 2
a + -0.2631578948 = -0.771730437 Simplifying a + -0.2631578948 = -0.771730437 Reorder the terms: -0.2631578948 + a = -0.771730437 Solving -0.2631578948 + a = -0.771730437 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2631578948' to each side of the equation. -0.2631578948 + 0.2631578948 + a = -0.771730437 + 0.2631578948 Combine like terms: -0.2631578948 + 0.2631578948 = 0.0000000000 0.0000000000 + a = -0.771730437 + 0.2631578948 a = -0.771730437 + 0.2631578948 Combine like terms: -0.771730437 + 0.2631578948 = -0.5085725422 a = -0.5085725422 Simplifying a = -0.5085725422Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.0348883318, -0.5085725422}
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