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Simplifying 3(a + 4) * a = 6 Reorder the terms: 3(4 + a) * a = 6 Reorder the terms for easier multiplication: 3a(4 + a) = 6 (4 * 3a + a * 3a) = 6 (12a + 3a2) = 6 Solving 12a + 3a2 = 6 Solving for variable 'a'. Reorder the terms: -6 + 12a + 3a2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 12a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 4a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 4a + a2)' equal to zero and attempt to solve: Simplifying -2 + 4a + a2 = 0 Solving -2 + 4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + 4a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4a + a2 = 0 + 2 4a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 4a + a2 = 2 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 + 4 Reorder the terms: 4 + 4a + a2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4a + a2 = 6 Factor a perfect square on the left side: (a + 2)(a + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (a + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
a + 2 = 2.449489743 Simplifying a + 2 = 2.449489743 Reorder the terms: 2 + a = 2.449489743 Solving 2 + a = 2.449489743 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 = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + a = 2.449489743 + -2 a = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 a = 0.449489743 Simplifying a = 0.449489743Subproblem 2
a + 2 = -2.449489743 Simplifying a + 2 = -2.449489743 Reorder the terms: 2 + a = -2.449489743 Solving 2 + a = -2.449489743 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 = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + a = -2.449489743 + -2 a = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 a = -4.449489743 Simplifying a = -4.449489743Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.449489743, -4.449489743}Solution
a = {0.449489743, -4.449489743}
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