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Simplifying 3a2 + 12a + -4 = 0 Reorder the terms: -4 + 12a + 3a2 = 0 Solving -4 + 12a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 4a + a2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 4a + 1.333333333 + a2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 4a + a2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 4a + a2 = 0 + 1.333333333 4a + a2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 4a + a2 = 1.333333333 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 1.333333333 + 4 Reorder the terms: 4 + 4a + a2 = 1.333333333 + 4 Combine like terms: 1.333333333 + 4 = 5.333333333 4 + 4a + a2 = 5.333333333 Factor a perfect square on the left side: (a + 2)(a + 2) = 5.333333333 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (a + 2) equal to 2.309401077 and -2.309401077.Subproblem 1
a + 2 = 2.309401077 Simplifying a + 2 = 2.309401077 Reorder the terms: 2 + a = 2.309401077 Solving 2 + a = 2.309401077 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 2.309401077 + -2 Combine like terms: 2 + -2 = 0 0 + a = 2.309401077 + -2 a = 2.309401077 + -2 Combine like terms: 2.309401077 + -2 = 0.309401077 a = 0.309401077 Simplifying a = 0.309401077Subproblem 2
a + 2 = -2.309401077 Simplifying a + 2 = -2.309401077 Reorder the terms: 2 + a = -2.309401077 Solving 2 + a = -2.309401077 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -2.309401077 + -2 Combine like terms: 2 + -2 = 0 0 + a = -2.309401077 + -2 a = -2.309401077 + -2 Combine like terms: -2.309401077 + -2 = -4.309401077 a = -4.309401077 Simplifying a = -4.309401077Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.309401077, -4.309401077}
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