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Simplifying 4a2 + 8a = 2 Reorder the terms: 8a + 4a2 = 2 Solving 8a + 4a2 = 2 Solving for variable 'a'. Reorder the terms: -2 + 8a + 4a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 8a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 4a + 2a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 4a + 2a2)' equal to zero and attempt to solve: Simplifying -1 + 4a + 2a2 = 0 Solving -1 + 4a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 2a + a2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2a + 0.5 + a2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2a + a2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2a + a2 = 0 + 0.5 2a + a2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2a + a2 = 0.5 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 0.5 + 1 Reorder the terms: 1 + 2a + a2 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + 2a + a2 = 1.5 Factor a perfect square on the left side: (a + 1)(a + 1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (a + 1) equal to 1.224744871 and -1.224744871.Subproblem 1
a + 1 = 1.224744871 Simplifying a + 1 = 1.224744871 Reorder the terms: 1 + a = 1.224744871 Solving 1 + a = 1.224744871 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + a = 1.224744871 + -1 a = 1.224744871 + -1 Combine like terms: 1.224744871 + -1 = 0.224744871 a = 0.224744871 Simplifying a = 0.224744871Subproblem 2
a + 1 = -1.224744871 Simplifying a + 1 = -1.224744871 Reorder the terms: 1 + a = -1.224744871 Solving 1 + a = -1.224744871 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -1.224744871 + -1 Combine like terms: 1 + -1 = 0 0 + a = -1.224744871 + -1 a = -1.224744871 + -1 Combine like terms: -1.224744871 + -1 = -2.224744871 a = -2.224744871 Simplifying a = -2.224744871Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.224744871, -2.224744871}Solution
a = {0.224744871, -2.224744871}
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