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Simplifying 6a2 + -33a + -4 = 0 Reorder the terms: -4 + -33a + 6a2 = 0 Solving -4 + -33a + 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'. -0.6666666667 + -5.5a + a2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -5.5a + 0.6666666667 + a2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -5.5a + a2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -5.5a + a2 = 0 + 0.6666666667 -5.5a + a2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -5.5a + a2 = 0.6666666667 The a term is -5.5a. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5a + 7.5625 + a2 = 0.6666666667 + 7.5625 Reorder the terms: 7.5625 + -5.5a + a2 = 0.6666666667 + 7.5625 Combine like terms: 0.6666666667 + 7.5625 = 8.2291666667 7.5625 + -5.5a + a2 = 8.2291666667 Factor a perfect square on the left side: (a + -2.75)(a + -2.75) = 8.2291666667 Calculate the square root of the right side: 2.868652413 Break this problem into two subproblems by setting (a + -2.75) equal to 2.868652413 and -2.868652413.Subproblem 1
a + -2.75 = 2.868652413 Simplifying a + -2.75 = 2.868652413 Reorder the terms: -2.75 + a = 2.868652413 Solving -2.75 + a = 2.868652413 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = 2.868652413 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = 2.868652413 + 2.75 a = 2.868652413 + 2.75 Combine like terms: 2.868652413 + 2.75 = 5.618652413 a = 5.618652413 Simplifying a = 5.618652413Subproblem 2
a + -2.75 = -2.868652413 Simplifying a + -2.75 = -2.868652413 Reorder the terms: -2.75 + a = -2.868652413 Solving -2.75 + a = -2.868652413 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = -2.868652413 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = -2.868652413 + 2.75 a = -2.868652413 + 2.75 Combine like terms: -2.868652413 + 2.75 = -0.118652413 a = -0.118652413 Simplifying a = -0.118652413Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.618652413, -0.118652413}
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