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Simplifying 2(3a2 + -5) = 6a + 4 Reorder the terms: 2(-5 + 3a2) = 6a + 4 (-5 * 2 + 3a2 * 2) = 6a + 4 (-10 + 6a2) = 6a + 4 Reorder the terms: -10 + 6a2 = 4 + 6a Solving -10 + 6a2 = 4 + 6a Solving for variable 'a'. Reorder the terms: -10 + -4 + -6a + 6a2 = 4 + 6a + -4 + -6a Combine like terms: -10 + -4 = -14 -14 + -6a + 6a2 = 4 + 6a + -4 + -6a Reorder the terms: -14 + -6a + 6a2 = 4 + -4 + 6a + -6a Combine like terms: 4 + -4 = 0 -14 + -6a + 6a2 = 0 + 6a + -6a -14 + -6a + 6a2 = 6a + -6a Combine like terms: 6a + -6a = 0 -14 + -6a + 6a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -3a + 3a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -3a + 3a2)' equal to zero and attempt to solve: Simplifying -7 + -3a + 3a2 = 0 Solving -7 + -3a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -1a + a2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -1a + 2.333333333 + a2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -1a + a2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -1a + a2 = 0 + 2.333333333 -1a + a2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -1a + a2 = 2.333333333 The a term is -1a. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = 2.333333333 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 2.333333333 + 0.25 Combine like terms: 2.333333333 + 0.25 = 2.583333333 0.25 + -1a + a2 = 2.583333333 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 2.583333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (a + -0.5) equal to 1.607275127 and -1.607275127.Subproblem 1
a + -0.5 = 1.607275127 Simplifying a + -0.5 = 1.607275127 Reorder the terms: -0.5 + a = 1.607275127 Solving -0.5 + a = 1.607275127 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 1.607275127 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 1.607275127 + 0.5 a = 1.607275127 + 0.5 Combine like terms: 1.607275127 + 0.5 = 2.107275127 a = 2.107275127 Simplifying a = 2.107275127Subproblem 2
a + -0.5 = -1.607275127 Simplifying a + -0.5 = -1.607275127 Reorder the terms: -0.5 + a = -1.607275127 Solving -0.5 + a = -1.607275127 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -1.607275127 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -1.607275127 + 0.5 a = -1.607275127 + 0.5 Combine like terms: -1.607275127 + 0.5 = -1.107275127 a = -1.107275127 Simplifying a = -1.107275127Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.107275127, -1.107275127}Solution
a = {2.107275127, -1.107275127}
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