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Simplifying 6a2 + -64a + -11 = 0 Reorder the terms: -11 + -64a + 6a2 = 0 Solving -11 + -64a + 6a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + -10.66666667a + a2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -10.66666667a + 1.833333333 + a2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -10.66666667a + a2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -10.66666667a + a2 = 0 + 1.833333333 -10.66666667a + a2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -10.66666667a + a2 = 1.833333333 The a term is -10.66666667a. Take half its coefficient (-5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. -10.66666667a + 28.44444446 + a2 = 1.833333333 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667a + a2 = 1.833333333 + 28.44444446 Combine like terms: 1.833333333 + 28.44444446 = 30.277777793 28.44444446 + -10.66666667a + a2 = 30.277777793 Factor a perfect square on the left side: (a + -5.333333335)(a + -5.333333335) = 30.277777793 Calculate the square root of the right side: 5.502524674 Break this problem into two subproblems by setting (a + -5.333333335) equal to 5.502524674 and -5.502524674.Subproblem 1
a + -5.333333335 = 5.502524674 Simplifying a + -5.333333335 = 5.502524674 Reorder the terms: -5.333333335 + a = 5.502524674 Solving -5.333333335 + a = 5.502524674 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + a = 5.502524674 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + a = 5.502524674 + 5.333333335 a = 5.502524674 + 5.333333335 Combine like terms: 5.502524674 + 5.333333335 = 10.835858009 a = 10.835858009 Simplifying a = 10.835858009Subproblem 2
a + -5.333333335 = -5.502524674 Simplifying a + -5.333333335 = -5.502524674 Reorder the terms: -5.333333335 + a = -5.502524674 Solving -5.333333335 + a = -5.502524674 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + a = -5.502524674 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + a = -5.502524674 + 5.333333335 a = -5.502524674 + 5.333333335 Combine like terms: -5.502524674 + 5.333333335 = -0.169191339 a = -0.169191339 Simplifying a = -0.169191339Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.835858009, -0.169191339}
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