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Simplifying 2a2 + -8a + -4 = 0 Reorder the terms: -4 + -8a + 2a2 = 0 Solving -4 + -8a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -4a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -4a + a2)' equal to zero and attempt to solve: Simplifying -2 + -4a + a2 = 0 Solving -2 + -4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -4a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -4a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4a + a2 = 0 + 2 -4a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4a + a2 = 2 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 2 + 4 Reorder the terms: 4 + -4a + a2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4a + a2 = 6 Factor a perfect square on the left side: (a + -2)(a + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (a + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
a + -2 = 2.449489743 Simplifying a + -2 = 2.449489743 Reorder the terms: -2 + a = 2.449489743 Solving -2 + a = 2.449489743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.449489743 + 2 a = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 a = 4.449489743 Simplifying a = 4.449489743Subproblem 2
a + -2 = -2.449489743 Simplifying a + -2 = -2.449489743 Reorder the terms: -2 + a = -2.449489743 Solving -2 + a = -2.449489743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.449489743 + 2 a = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 a = -0.449489743 Simplifying a = -0.449489743Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.449489743, -0.449489743}Solution
a = {4.449489743, -0.449489743}
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