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Simplifying 11a2 + -3 = 4a Reorder the terms: -3 + 11a2 = 4a Solving -3 + 11a2 = 4a Solving for variable 'a'. Reorder the terms: -3 + -4a + 11a2 = 4a + -4a Combine like terms: 4a + -4a = 0 -3 + -4a + 11a2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.2727272727 + -0.3636363636a + a2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.3636363636a + 0.2727272727 + a2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.3636363636a + a2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.3636363636a + a2 = 0 + 0.2727272727 -0.3636363636a + a2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.3636363636a + a2 = 0.2727272727 The a term is -0.3636363636a. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636a + 0.03305785123 + a2 = 0.2727272727 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636a + a2 = 0.2727272727 + 0.03305785123 Combine like terms: 0.2727272727 + 0.03305785123 = 0.30578512393 0.03305785123 + -0.3636363636a + a2 = 0.30578512393 Factor a perfect square on the left side: (a + -0.1818181818)(a + -0.1818181818) = 0.30578512393 Calculate the square root of the right side: 0.552978412 Break this problem into two subproblems by setting (a + -0.1818181818) equal to 0.552978412 and -0.552978412.Subproblem 1
a + -0.1818181818 = 0.552978412 Simplifying a + -0.1818181818 = 0.552978412 Reorder the terms: -0.1818181818 + a = 0.552978412 Solving -0.1818181818 + a = 0.552978412 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + a = 0.552978412 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + a = 0.552978412 + 0.1818181818 a = 0.552978412 + 0.1818181818 Combine like terms: 0.552978412 + 0.1818181818 = 0.7347965938 a = 0.7347965938 Simplifying a = 0.7347965938Subproblem 2
a + -0.1818181818 = -0.552978412 Simplifying a + -0.1818181818 = -0.552978412 Reorder the terms: -0.1818181818 + a = -0.552978412 Solving -0.1818181818 + a = -0.552978412 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + a = -0.552978412 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + a = -0.552978412 + 0.1818181818 a = -0.552978412 + 0.1818181818 Combine like terms: -0.552978412 + 0.1818181818 = -0.3711602302 a = -0.3711602302 Simplifying a = -0.3711602302Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.7347965938, -0.3711602302}
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