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Simplifying 6a2 + -6a + -5 = 0 Reorder the terms: -5 + -6a + 6a2 = 0 Solving -5 + -6a + 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'. -0.8333333333 + -1a + a2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -1a + 0.8333333333 + a2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -1a + a2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -1a + a2 = 0 + 0.8333333333 -1a + a2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -1a + a2 = 0.8333333333 The a term is -1a. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = 0.8333333333 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 0.8333333333 + 0.25 Combine like terms: 0.8333333333 + 0.25 = 1.0833333333 0.25 + -1a + a2 = 1.0833333333 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 1.0833333333 Calculate the square root of the right side: 1.040833 Break this problem into two subproblems by setting (a + -0.5) equal to 1.040833 and -1.040833.Subproblem 1
a + -0.5 = 1.040833 Simplifying a + -0.5 = 1.040833 Reorder the terms: -0.5 + a = 1.040833 Solving -0.5 + a = 1.040833 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 1.040833 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 1.040833 + 0.5 a = 1.040833 + 0.5 Combine like terms: 1.040833 + 0.5 = 1.540833 a = 1.540833 Simplifying a = 1.540833Subproblem 2
a + -0.5 = -1.040833 Simplifying a + -0.5 = -1.040833 Reorder the terms: -0.5 + a = -1.040833 Solving -0.5 + a = -1.040833 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -1.040833 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -1.040833 + 0.5 a = -1.040833 + 0.5 Combine like terms: -1.040833 + 0.5 = -0.540833 a = -0.540833 Simplifying a = -0.540833Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.540833, -0.540833}
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