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Simplifying 6a(a + -6 * 2) = 18 Multiply -6 * 2 6a(a + -12) = 18 Reorder the terms: 6a(-12 + a) = 18 (-12 * 6a + a * 6a) = 18 (-72a + 6a2) = 18 Solving -72a + 6a2 = 18 Solving for variable 'a'. Reorder the terms: -18 + -72a + 6a2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -72a + 6a2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + -12a + a2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + -12a + a2)' equal to zero and attempt to solve: Simplifying -3 + -12a + a2 = 0 Solving -3 + -12a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -12a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + -12a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -12a + a2 = 0 + 3 -12a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 -12a + a2 = 3 The a term is -12a. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a + 36 + a2 = 3 + 36 Reorder the terms: 36 + -12a + a2 = 3 + 36 Combine like terms: 3 + 36 = 39 36 + -12a + a2 = 39 Factor a perfect square on the left side: (a + -6)(a + -6) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (a + -6) equal to 6.244997998 and -6.244997998.Subproblem 1
a + -6 = 6.244997998 Simplifying a + -6 = 6.244997998 Reorder the terms: -6 + a = 6.244997998 Solving -6 + a = 6.244997998 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 6.244997998 + 6 Combine like terms: -6 + 6 = 0 0 + a = 6.244997998 + 6 a = 6.244997998 + 6 Combine like terms: 6.244997998 + 6 = 12.244997998 a = 12.244997998 Simplifying a = 12.244997998Subproblem 2
a + -6 = -6.244997998 Simplifying a + -6 = -6.244997998 Reorder the terms: -6 + a = -6.244997998 Solving -6 + a = -6.244997998 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = -6.244997998 + 6 Combine like terms: -6 + 6 = 0 0 + a = -6.244997998 + 6 a = -6.244997998 + 6 Combine like terms: -6.244997998 + 6 = -0.244997998 a = -0.244997998 Simplifying a = -0.244997998Solution
The solution to the problem is based on the solutions from the subproblems. a = {12.244997998, -0.244997998}Solution
a = {12.244997998, -0.244997998}
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