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Simplifying (2a3 + -1a + -4a2) = 0 Reorder the terms: (-1a + -4a2 + 2a3) = 0 Remove parenthesis around (-1a + -4a2 + 2a3) -1a + -4a2 + 2a3 = 0 Solving -1a + -4a2 + 2a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-1 + -4a + 2a2) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
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 = 2.224744871 a = 2.224744871 Simplifying a = 2.224744871Subproblem 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 = -0.224744871 a = -0.224744871 Simplifying a = -0.224744871Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.224744871, -0.224744871}Solution
a = {0, 2.224744871, -0.224744871}
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