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Simplifying 2a2 + -16a + 8 = 0 Reorder the terms: 8 + -16a + 2a2 = 0 Solving 8 + -16a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -8a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -8a + a2)' equal to zero and attempt to solve: Simplifying 4 + -8a + a2 = 0 Solving 4 + -8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -8a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + -8a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -8a + a2 = 0 + -4 -8a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -8a + a2 = -4 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = -4 + 16 Reorder the terms: 16 + -8a + a2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + -8a + a2 = 12 Factor a perfect square on the left side: (a + -4)(a + -4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (a + -4) equal to 3.464101615 and -3.464101615.Subproblem 1
a + -4 = 3.464101615 Simplifying a + -4 = 3.464101615 Reorder the terms: -4 + a = 3.464101615 Solving -4 + a = 3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + a = 3.464101615 + 4 a = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 a = 7.464101615 Simplifying a = 7.464101615Subproblem 2
a + -4 = -3.464101615 Simplifying a + -4 = -3.464101615 Reorder the terms: -4 + a = -3.464101615 Solving -4 + a = -3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + a = -3.464101615 + 4 a = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 a = 0.535898385 Simplifying a = 0.535898385Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.464101615, 0.535898385}Solution
a = {7.464101615, 0.535898385}
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