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Simplifying 12a2 + -6 = -5a Reorder the terms: -6 + 12a2 = -5a Solving -6 + 12a2 = -5a Solving for variable 'a'. Reorder the terms: -6 + 5a + 12a2 = -5a + 5a Combine like terms: -5a + 5a = 0 -6 + 5a + 12a2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5 + 0.4166666667a + a2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.4166666667a + 0.5 + a2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.4166666667a + a2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.4166666667a + a2 = 0 + 0.5 0.4166666667a + a2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.4166666667a + a2 = 0.5 The a term is 0.4166666667a. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667a + 0.04340277781 + a2 = 0.5 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667a + a2 = 0.5 + 0.04340277781 Combine like terms: 0.5 + 0.04340277781 = 0.54340277781 0.04340277781 + 0.4166666667a + a2 = 0.54340277781 Factor a perfect square on the left side: (a + 0.2083333334)(a + 0.2083333334) = 0.54340277781 Calculate the square root of the right side: 0.737158584 Break this problem into two subproblems by setting (a + 0.2083333334) equal to 0.737158584 and -0.737158584.Subproblem 1
a + 0.2083333334 = 0.737158584 Simplifying a + 0.2083333334 = 0.737158584 Reorder the terms: 0.2083333334 + a = 0.737158584 Solving 0.2083333334 + a = 0.737158584 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + a = 0.737158584 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + a = 0.737158584 + -0.2083333334 a = 0.737158584 + -0.2083333334 Combine like terms: 0.737158584 + -0.2083333334 = 0.5288252506 a = 0.5288252506 Simplifying a = 0.5288252506Subproblem 2
a + 0.2083333334 = -0.737158584 Simplifying a + 0.2083333334 = -0.737158584 Reorder the terms: 0.2083333334 + a = -0.737158584 Solving 0.2083333334 + a = -0.737158584 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + a = -0.737158584 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + a = -0.737158584 + -0.2083333334 a = -0.737158584 + -0.2083333334 Combine like terms: -0.737158584 + -0.2083333334 = -0.9454919174 a = -0.9454919174 Simplifying a = -0.9454919174Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.5288252506, -0.9454919174}
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