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Simplifying 3a2 + -12a + 3 = -4 Reorder the terms: 3 + -12a + 3a2 = -4 Solving 3 + -12a + 3a2 = -4 Solving for variable 'a'. Reorder the terms: 3 + 4 + -12a + 3a2 = -4 + 4 Combine like terms: 3 + 4 = 7 7 + -12a + 3a2 = -4 + 4 Combine like terms: -4 + 4 = 0 7 + -12a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -4a + a2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -4a + -2.333333333 + a2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -4a + a2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -4a + a2 = 0 + -2.333333333 -4a + a2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -4a + a2 = -2.333333333 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 = -2.333333333 + 4 Reorder the terms: 4 + -4a + a2 = -2.333333333 + 4 Combine like terms: -2.333333333 + 4 = 1.666666667 4 + -4a + a2 = 1.666666667 Factor a perfect square on the left side: (a + -2)(a + -2) = 1.666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (a + -2) equal to 1.290994449 and -1.290994449.Subproblem 1
a + -2 = 1.290994449 Simplifying a + -2 = 1.290994449 Reorder the terms: -2 + a = 1.290994449 Solving -2 + a = 1.290994449 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 = 1.290994449 + 2 Combine like terms: -2 + 2 = 0 0 + a = 1.290994449 + 2 a = 1.290994449 + 2 Combine like terms: 1.290994449 + 2 = 3.290994449 a = 3.290994449 Simplifying a = 3.290994449Subproblem 2
a + -2 = -1.290994449 Simplifying a + -2 = -1.290994449 Reorder the terms: -2 + a = -1.290994449 Solving -2 + a = -1.290994449 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 = -1.290994449 + 2 Combine like terms: -2 + 2 = 0 0 + a = -1.290994449 + 2 a = -1.290994449 + 2 Combine like terms: -1.290994449 + 2 = 0.709005551 a = 0.709005551 Simplifying a = 0.709005551Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.290994449, 0.709005551}
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