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Simplifying 6a * a + -3a + -2 = 0 Multiply a * a 6a2 + -3a + -2 = 0 Reorder the terms: -2 + -3a + 6a2 = 0 Solving -2 + -3a + 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'. -0.3333333333 + -0.5a + a2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.5a + 0.3333333333 + a2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.5a + a2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.5a + a2 = 0 + 0.3333333333 -0.5a + a2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.5a + a2 = 0.3333333333 The a term is -0.5a. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a + 0.0625 + a2 = 0.3333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = 0.3333333333 + 0.0625 Combine like terms: 0.3333333333 + 0.0625 = 0.3958333333 0.0625 + -0.5a + a2 = 0.3958333333 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = 0.3958333333 Calculate the square root of the right side: 0.62915287 Break this problem into two subproblems by setting (a + -0.25) equal to 0.62915287 and -0.62915287.Subproblem 1
a + -0.25 = 0.62915287 Simplifying a + -0.25 = 0.62915287 Reorder the terms: -0.25 + a = 0.62915287 Solving -0.25 + a = 0.62915287 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 0.62915287 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 0.62915287 + 0.25 a = 0.62915287 + 0.25 Combine like terms: 0.62915287 + 0.25 = 0.87915287 a = 0.87915287 Simplifying a = 0.87915287Subproblem 2
a + -0.25 = -0.62915287 Simplifying a + -0.25 = -0.62915287 Reorder the terms: -0.25 + a = -0.62915287 Solving -0.25 + a = -0.62915287 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -0.62915287 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -0.62915287 + 0.25 a = -0.62915287 + 0.25 Combine like terms: -0.62915287 + 0.25 = -0.37915287 a = -0.37915287 Simplifying a = -0.37915287Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.87915287, -0.37915287}
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