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Simplifying 7a2 + -5a + -1 = 0 Reorder the terms: -1 + -5a + 7a2 = 0 Solving -1 + -5a + 7a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.7142857143a + a2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.7142857143a + 0.1428571429 + a2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.7142857143a + a2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.7142857143a + a2 = 0 + 0.1428571429 -0.7142857143a + a2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.7142857143a + a2 = 0.1428571429 The a term is -0.7142857143a. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143a + 0.1275510204 + a2 = 0.1428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143a + a2 = 0.1428571429 + 0.1275510204 Combine like terms: 0.1428571429 + 0.1275510204 = 0.2704081633 0.1275510204 + -0.7142857143a + a2 = 0.2704081633 Factor a perfect square on the left side: (a + -0.3571428572)(a + -0.3571428572) = 0.2704081633 Calculate the square root of the right side: 0.520007849 Break this problem into two subproblems by setting (a + -0.3571428572) equal to 0.520007849 and -0.520007849.Subproblem 1
a + -0.3571428572 = 0.520007849 Simplifying a + -0.3571428572 = 0.520007849 Reorder the terms: -0.3571428572 + a = 0.520007849 Solving -0.3571428572 + a = 0.520007849 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + a = 0.520007849 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + a = 0.520007849 + 0.3571428572 a = 0.520007849 + 0.3571428572 Combine like terms: 0.520007849 + 0.3571428572 = 0.8771507062 a = 0.8771507062 Simplifying a = 0.8771507062Subproblem 2
a + -0.3571428572 = -0.520007849 Simplifying a + -0.3571428572 = -0.520007849 Reorder the terms: -0.3571428572 + a = -0.520007849 Solving -0.3571428572 + a = -0.520007849 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + a = -0.520007849 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + a = -0.520007849 + 0.3571428572 a = -0.520007849 + 0.3571428572 Combine like terms: -0.520007849 + 0.3571428572 = -0.1628649918 a = -0.1628649918 Simplifying a = -0.1628649918Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.8771507062, -0.1628649918}
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