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Simplifying 3a2 + -12a = 5 Reorder the terms: -12a + 3a2 = 5 Solving -12a + 3a2 = 5 Solving for variable 'a'. Reorder the terms: -5 + -12a + 3a2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -12a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + -4a + a2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -4a + 1.666666667 + a2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -4a + a2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -4a + a2 = 0 + 1.666666667 -4a + a2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -4a + a2 = 1.666666667 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 = 1.666666667 + 4 Reorder the terms: 4 + -4a + a2 = 1.666666667 + 4 Combine like terms: 1.666666667 + 4 = 5.666666667 4 + -4a + a2 = 5.666666667 Factor a perfect square on the left side: (a + -2)(a + -2) = 5.666666667 Calculate the square root of the right side: 2.380476143 Break this problem into two subproblems by setting (a + -2) equal to 2.380476143 and -2.380476143.Subproblem 1
a + -2 = 2.380476143 Simplifying a + -2 = 2.380476143 Reorder the terms: -2 + a = 2.380476143 Solving -2 + a = 2.380476143 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 = 2.380476143 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.380476143 + 2 a = 2.380476143 + 2 Combine like terms: 2.380476143 + 2 = 4.380476143 a = 4.380476143 Simplifying a = 4.380476143Subproblem 2
a + -2 = -2.380476143 Simplifying a + -2 = -2.380476143 Reorder the terms: -2 + a = -2.380476143 Solving -2 + a = -2.380476143 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 = -2.380476143 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.380476143 + 2 a = -2.380476143 + 2 Combine like terms: -2.380476143 + 2 = -0.380476143 a = -0.380476143 Simplifying a = -0.380476143Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.380476143, -0.380476143}
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