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Simplifying 3a2 + -23 + -12a = 0 Reorder the terms: -23 + -12a + 3a2 = 0 Solving -23 + -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'. -7.666666667 + -4a + a2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + -4a + 7.666666667 + a2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + -4a + a2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + -4a + a2 = 0 + 7.666666667 -4a + a2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 -4a + a2 = 7.666666667 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 = 7.666666667 + 4 Reorder the terms: 4 + -4a + a2 = 7.666666667 + 4 Combine like terms: 7.666666667 + 4 = 11.666666667 4 + -4a + a2 = 11.666666667 Factor a perfect square on the left side: (a + -2)(a + -2) = 11.666666667 Calculate the square root of the right side: 3.415650255 Break this problem into two subproblems by setting (a + -2) equal to 3.415650255 and -3.415650255.Subproblem 1
a + -2 = 3.415650255 Simplifying a + -2 = 3.415650255 Reorder the terms: -2 + a = 3.415650255 Solving -2 + a = 3.415650255 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 = 3.415650255 + 2 Combine like terms: -2 + 2 = 0 0 + a = 3.415650255 + 2 a = 3.415650255 + 2 Combine like terms: 3.415650255 + 2 = 5.415650255 a = 5.415650255 Simplifying a = 5.415650255Subproblem 2
a + -2 = -3.415650255 Simplifying a + -2 = -3.415650255 Reorder the terms: -2 + a = -3.415650255 Solving -2 + a = -3.415650255 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 = -3.415650255 + 2 Combine like terms: -2 + 2 = 0 0 + a = -3.415650255 + 2 a = -3.415650255 + 2 Combine like terms: -3.415650255 + 2 = -1.415650255 a = -1.415650255 Simplifying a = -1.415650255Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.415650255, -1.415650255}
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