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Simplifying 8a(8 + -1a) + 64 = 8 (8 * 8a + -1a * 8a) + 64 = 8 (64a + -8a2) + 64 = 8 Reorder the terms: 64 + 64a + -8a2 = 8 Solving 64 + 64a + -8a2 = 8 Solving for variable 'a'. Reorder the terms: 64 + -8 + 64a + -8a2 = 8 + -8 Combine like terms: 64 + -8 = 56 56 + 64a + -8a2 = 8 + -8 Combine like terms: 8 + -8 = 0 56 + 64a + -8a2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(7 + 8a + -1a2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(7 + 8a + -1a2)' equal to zero and attempt to solve: Simplifying 7 + 8a + -1a2 = 0 Solving 7 + 8a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -8a + a2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -8a + 7 + a2 = 0 + 7 Reorder the terms: -7 + 7 + -8a + a2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8a + a2 = 0 + 7 -8a + a2 = 0 + 7 Combine like terms: 0 + 7 = 7 -8a + a2 = 7 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 = 7 + 16 Reorder the terms: 16 + -8a + a2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + -8a + a2 = 23 Factor a perfect square on the left side: (a + -4)(a + -4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (a + -4) equal to 4.795831523 and -4.795831523.Subproblem 1
a + -4 = 4.795831523 Simplifying a + -4 = 4.795831523 Reorder the terms: -4 + a = 4.795831523 Solving -4 + a = 4.795831523 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 = 4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + a = 4.795831523 + 4 a = 4.795831523 + 4 Combine like terms: 4.795831523 + 4 = 8.795831523 a = 8.795831523 Simplifying a = 8.795831523Subproblem 2
a + -4 = -4.795831523 Simplifying a + -4 = -4.795831523 Reorder the terms: -4 + a = -4.795831523 Solving -4 + a = -4.795831523 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 = -4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + a = -4.795831523 + 4 a = -4.795831523 + 4 Combine like terms: -4.795831523 + 4 = -0.795831523 a = -0.795831523 Simplifying a = -0.795831523Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.795831523, -0.795831523}Solution
a = {8.795831523, -0.795831523}
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