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Simplifying 9a2 + -5a + -12 = 0 Reorder the terms: -12 + -5a + 9a2 = 0 Solving -12 + -5a + 9a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.333333333 + -0.5555555556a + a2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.5555555556a + 1.333333333 + a2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.5555555556a + a2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.5555555556a + a2 = 0 + 1.333333333 -0.5555555556a + a2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.5555555556a + a2 = 1.333333333 The a term is -0.5555555556a. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556a + 0.07716049384 + a2 = 1.333333333 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556a + a2 = 1.333333333 + 0.07716049384 Combine like terms: 1.333333333 + 0.07716049384 = 1.41049382684 0.07716049384 + -0.5555555556a + a2 = 1.41049382684 Factor a perfect square on the left side: (a + -0.2777777778)(a + -0.2777777778) = 1.41049382684 Calculate the square root of the right side: 1.187642129 Break this problem into two subproblems by setting (a + -0.2777777778) equal to 1.187642129 and -1.187642129.Subproblem 1
a + -0.2777777778 = 1.187642129 Simplifying a + -0.2777777778 = 1.187642129 Reorder the terms: -0.2777777778 + a = 1.187642129 Solving -0.2777777778 + a = 1.187642129 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + a = 1.187642129 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + a = 1.187642129 + 0.2777777778 a = 1.187642129 + 0.2777777778 Combine like terms: 1.187642129 + 0.2777777778 = 1.4654199068 a = 1.4654199068 Simplifying a = 1.4654199068Subproblem 2
a + -0.2777777778 = -1.187642129 Simplifying a + -0.2777777778 = -1.187642129 Reorder the terms: -0.2777777778 + a = -1.187642129 Solving -0.2777777778 + a = -1.187642129 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + a = -1.187642129 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + a = -1.187642129 + 0.2777777778 a = -1.187642129 + 0.2777777778 Combine like terms: -1.187642129 + 0.2777777778 = -0.9098643512 a = -0.9098643512 Simplifying a = -0.9098643512Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.4654199068, -0.9098643512}
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