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Simplifying 12a2 + -5a + -12 = 0 Reorder the terms: -12 + -5a + 12a2 = 0 Solving -12 + -5a + 12a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1 + -0.4166666667a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.4166666667a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + -0.4166666667a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.4166666667a + a2 = 0 + 1 -0.4166666667a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.4166666667a + a2 = 1 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 = 1 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667a + a2 = 1 + 0.04340277781 Combine like terms: 1 + 0.04340277781 = 1.04340277781 0.04340277781 + -0.4166666667a + a2 = 1.04340277781 Factor a perfect square on the left side: (a + -0.2083333334)(a + -0.2083333334) = 1.04340277781 Calculate the square root of the right side: 1.021470889 Break this problem into two subproblems by setting (a + -0.2083333334) equal to 1.021470889 and -1.021470889.Subproblem 1
a + -0.2083333334 = 1.021470889 Simplifying a + -0.2083333334 = 1.021470889 Reorder the terms: -0.2083333334 + a = 1.021470889 Solving -0.2083333334 + a = 1.021470889 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 = 1.021470889 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + a = 1.021470889 + 0.2083333334 a = 1.021470889 + 0.2083333334 Combine like terms: 1.021470889 + 0.2083333334 = 1.2298042224 a = 1.2298042224 Simplifying a = 1.2298042224Subproblem 2
a + -0.2083333334 = -1.021470889 Simplifying a + -0.2083333334 = -1.021470889 Reorder the terms: -0.2083333334 + a = -1.021470889 Solving -0.2083333334 + a = -1.021470889 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 = -1.021470889 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + a = -1.021470889 + 0.2083333334 a = -1.021470889 + 0.2083333334 Combine like terms: -1.021470889 + 0.2083333334 = -0.8131375556 a = -0.8131375556 Simplifying a = -0.8131375556Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.2298042224, -0.8131375556}
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