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Simplifying 3a2 + -36a + 91 = 0 Reorder the terms: 91 + -36a + 3a2 = 0 Solving 91 + -36a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 30.33333333 + -12a + a2 = 0 Move the constant term to the right: Add '-30.33333333' to each side of the equation. 30.33333333 + -12a + -30.33333333 + a2 = 0 + -30.33333333 Reorder the terms: 30.33333333 + -30.33333333 + -12a + a2 = 0 + -30.33333333 Combine like terms: 30.33333333 + -30.33333333 = 0.00000000 0.00000000 + -12a + a2 = 0 + -30.33333333 -12a + a2 = 0 + -30.33333333 Combine like terms: 0 + -30.33333333 = -30.33333333 -12a + a2 = -30.33333333 The a term is -12a. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a + 36 + a2 = -30.33333333 + 36 Reorder the terms: 36 + -12a + a2 = -30.33333333 + 36 Combine like terms: -30.33333333 + 36 = 5.66666667 36 + -12a + a2 = 5.66666667 Factor a perfect square on the left side: (a + -6)(a + -6) = 5.66666667 Calculate the square root of the right side: 2.380476144 Break this problem into two subproblems by setting (a + -6) equal to 2.380476144 and -2.380476144.Subproblem 1
a + -6 = 2.380476144 Simplifying a + -6 = 2.380476144 Reorder the terms: -6 + a = 2.380476144 Solving -6 + a = 2.380476144 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 2.380476144 + 6 Combine like terms: -6 + 6 = 0 0 + a = 2.380476144 + 6 a = 2.380476144 + 6 Combine like terms: 2.380476144 + 6 = 8.380476144 a = 8.380476144 Simplifying a = 8.380476144Subproblem 2
a + -6 = -2.380476144 Simplifying a + -6 = -2.380476144 Reorder the terms: -6 + a = -2.380476144 Solving -6 + a = -2.380476144 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = -2.380476144 + 6 Combine like terms: -6 + 6 = 0 0 + a = -2.380476144 + 6 a = -2.380476144 + 6 Combine like terms: -2.380476144 + 6 = 3.619523856 a = 3.619523856 Simplifying a = 3.619523856Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.380476144, 3.619523856}
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