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Simplifying 3a2 + -12a + 3 = a2 + -4 Reorder the terms: 3 + -12a + 3a2 = a2 + -4 Reorder the terms: 3 + -12a + 3a2 = -4 + a2 Solving 3 + -12a + 3a2 = -4 + a2 Solving for variable 'a'. Reorder the terms: 3 + 4 + -12a + 3a2 + -1a2 = -4 + a2 + 4 + -1a2 Combine like terms: 3 + 4 = 7 7 + -12a + 3a2 + -1a2 = -4 + a2 + 4 + -1a2 Combine like terms: 3a2 + -1a2 = 2a2 7 + -12a + 2a2 = -4 + a2 + 4 + -1a2 Reorder the terms: 7 + -12a + 2a2 = -4 + 4 + a2 + -1a2 Combine like terms: -4 + 4 = 0 7 + -12a + 2a2 = 0 + a2 + -1a2 7 + -12a + 2a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 7 + -12a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -6a + a2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -6a + -3.5 + a2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -6a + a2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -6a + a2 = 0 + -3.5 -6a + a2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -6a + a2 = -3.5 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = -3.5 + 9 Reorder the terms: 9 + -6a + a2 = -3.5 + 9 Combine like terms: -3.5 + 9 = 5.5 9 + -6a + a2 = 5.5 Factor a perfect square on the left side: (a + -3)(a + -3) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (a + -3) equal to 2.34520788 and -2.34520788.Subproblem 1
a + -3 = 2.34520788 Simplifying a + -3 = 2.34520788 Reorder the terms: -3 + a = 2.34520788 Solving -3 + a = 2.34520788 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + a = 2.34520788 + 3 a = 2.34520788 + 3 Combine like terms: 2.34520788 + 3 = 5.34520788 a = 5.34520788 Simplifying a = 5.34520788Subproblem 2
a + -3 = -2.34520788 Simplifying a + -3 = -2.34520788 Reorder the terms: -3 + a = -2.34520788 Solving -3 + a = -2.34520788 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + a = -2.34520788 + 3 a = -2.34520788 + 3 Combine like terms: -2.34520788 + 3 = 0.65479212 a = 0.65479212 Simplifying a = 0.65479212Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.34520788, 0.65479212}
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