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Simplifying 3(2a + 5) + 2(3 + -1a) * a = 4 Reorder the terms: 3(5 + 2a) + 2(3 + -1a) * a = 4 (5 * 3 + 2a * 3) + 2(3 + -1a) * a = 4 (15 + 6a) + 2(3 + -1a) * a = 4 Reorder the terms for easier multiplication: 15 + 6a + 2a(3 + -1a) = 4 15 + 6a + (3 * 2a + -1a * 2a) = 4 15 + 6a + (6a + -2a2) = 4 Combine like terms: 6a + 6a = 12a 15 + 12a + -2a2 = 4 Solving 15 + 12a + -2a2 = 4 Solving for variable 'a'. Reorder the terms: 15 + -4 + 12a + -2a2 = 4 + -4 Combine like terms: 15 + -4 = 11 11 + 12a + -2a2 = 4 + -4 Combine like terms: 4 + -4 = 0 11 + 12a + -2a2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5.5 + -6a + a2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -6a + 5.5 + a2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -6a + a2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -6a + a2 = 0 + 5.5 -6a + a2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -6a + a2 = 5.5 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = 5.5 + 9 Reorder the terms: 9 + -6a + a2 = 5.5 + 9 Combine like terms: 5.5 + 9 = 14.5 9 + -6a + a2 = 14.5 Factor a perfect square on the left side: (a + -3)(a + -3) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (a + -3) equal to 3.807886553 and -3.807886553.Subproblem 1
a + -3 = 3.807886553 Simplifying a + -3 = 3.807886553 Reorder the terms: -3 + a = 3.807886553 Solving -3 + a = 3.807886553 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + a = 3.807886553 + 3 a = 3.807886553 + 3 Combine like terms: 3.807886553 + 3 = 6.807886553 a = 6.807886553 Simplifying a = 6.807886553Subproblem 2
a + -3 = -3.807886553 Simplifying a + -3 = -3.807886553 Reorder the terms: -3 + a = -3.807886553 Solving -3 + a = -3.807886553 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + a = -3.807886553 + 3 a = -3.807886553 + 3 Combine like terms: -3.807886553 + 3 = -0.807886553 a = -0.807886553 Simplifying a = -0.807886553Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.807886553, -0.807886553}
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