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Simplifying -8a + 6a2 + -2 + 2a2 = 0 Reorder the terms: -2 + -8a + 6a2 + 2a2 = 0 Combine like terms: 6a2 + 2a2 = 8a2 -2 + -8a + 8a2 = 0 Solving -2 + -8a + 8a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -4a + 4a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4a + 4a2)' equal to zero and attempt to solve: Simplifying -1 + -4a + 4a2 = 0 Solving -1 + -4a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -1a + a2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1a + 0.25 + a2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1a + a2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1a + a2 = 0 + 0.25 -1a + a2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1a + a2 = 0.25 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 = 0.25 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 0.25 + 0.25 Combine like terms: 0.25 + 0.25 = 0.5 0.25 + -1a + a2 = 0.5 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (a + -0.5) equal to 0.707106781 and -0.707106781.Subproblem 1
a + -0.5 = 0.707106781 Simplifying a + -0.5 = 0.707106781 Reorder the terms: -0.5 + a = 0.707106781 Solving -0.5 + a = 0.707106781 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 = 0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 0.707106781 + 0.5 a = 0.707106781 + 0.5 Combine like terms: 0.707106781 + 0.5 = 1.207106781 a = 1.207106781 Simplifying a = 1.207106781Subproblem 2
a + -0.5 = -0.707106781 Simplifying a + -0.5 = -0.707106781 Reorder the terms: -0.5 + a = -0.707106781 Solving -0.5 + a = -0.707106781 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 = -0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -0.707106781 + 0.5 a = -0.707106781 + 0.5 Combine like terms: -0.707106781 + 0.5 = -0.207106781 a = -0.207106781 Simplifying a = -0.207106781Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.207106781, -0.207106781}Solution
a = {1.207106781, -0.207106781}
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