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Simplifying 3a2 + -12a = 16 Reorder the terms: -12a + 3a2 = 16 Solving -12a + 3a2 = 16 Solving for variable 'a'. Reorder the terms: -16 + -12a + 3a2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -12a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -4a + a2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -4a + 5.333333333 + a2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -4a + a2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -4a + a2 = 0 + 5.333333333 -4a + a2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -4a + a2 = 5.333333333 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 = 5.333333333 + 4 Reorder the terms: 4 + -4a + a2 = 5.333333333 + 4 Combine like terms: 5.333333333 + 4 = 9.333333333 4 + -4a + a2 = 9.333333333 Factor a perfect square on the left side: (a + -2)(a + -2) = 9.333333333 Calculate the square root of the right side: 3.055050463 Break this problem into two subproblems by setting (a + -2) equal to 3.055050463 and -3.055050463.Subproblem 1
a + -2 = 3.055050463 Simplifying a + -2 = 3.055050463 Reorder the terms: -2 + a = 3.055050463 Solving -2 + a = 3.055050463 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 = 3.055050463 + 2 Combine like terms: -2 + 2 = 0 0 + a = 3.055050463 + 2 a = 3.055050463 + 2 Combine like terms: 3.055050463 + 2 = 5.055050463 a = 5.055050463 Simplifying a = 5.055050463Subproblem 2
a + -2 = -3.055050463 Simplifying a + -2 = -3.055050463 Reorder the terms: -2 + a = -3.055050463 Solving -2 + a = -3.055050463 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 = -3.055050463 + 2 Combine like terms: -2 + 2 = 0 0 + a = -3.055050463 + 2 a = -3.055050463 + 2 Combine like terms: -3.055050463 + 2 = -1.055050463 a = -1.055050463 Simplifying a = -1.055050463Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.055050463, -1.055050463}
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