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Simplifying 3a2 + -12a = 10 Reorder the terms: -12a + 3a2 = 10 Solving -12a + 3a2 = 10 Solving for variable 'a'. Reorder the terms: -10 + -12a + 3a2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -12a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -4a + a2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -4a + 3.333333333 + a2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -4a + a2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -4a + a2 = 0 + 3.333333333 -4a + a2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -4a + a2 = 3.333333333 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 = 3.333333333 + 4 Reorder the terms: 4 + -4a + a2 = 3.333333333 + 4 Combine like terms: 3.333333333 + 4 = 7.333333333 4 + -4a + a2 = 7.333333333 Factor a perfect square on the left side: (a + -2)(a + -2) = 7.333333333 Calculate the square root of the right side: 2.708012801 Break this problem into two subproblems by setting (a + -2) equal to 2.708012801 and -2.708012801.Subproblem 1
a + -2 = 2.708012801 Simplifying a + -2 = 2.708012801 Reorder the terms: -2 + a = 2.708012801 Solving -2 + a = 2.708012801 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 = 2.708012801 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.708012801 + 2 a = 2.708012801 + 2 Combine like terms: 2.708012801 + 2 = 4.708012801 a = 4.708012801 Simplifying a = 4.708012801Subproblem 2
a + -2 = -2.708012801 Simplifying a + -2 = -2.708012801 Reorder the terms: -2 + a = -2.708012801 Solving -2 + a = -2.708012801 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 = -2.708012801 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.708012801 + 2 a = -2.708012801 + 2 Combine like terms: -2.708012801 + 2 = -0.708012801 a = -0.708012801 Simplifying a = -0.708012801Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.708012801, -0.708012801}
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