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Simplifying -2a(a + 16) = 2 Reorder the terms: -2a(16 + a) = 2 (16 * -2a + a * -2a) = 2 (-32a + -2a2) = 2 Solving -32a + -2a2 = 2 Solving for variable 'a'. Reorder the terms: -2 + -32a + -2a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -32a + -2a2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + 16a + a2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1 + 16a + a2)' equal to zero and attempt to solve: Simplifying 1 + 16a + a2 = 0 Solving 1 + 16a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 16a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + 16a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 16a + a2 = 0 + -1 16a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 16a + a2 = -1 The a term is 16a. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16a + 64 + a2 = -1 + 64 Reorder the terms: 64 + 16a + a2 = -1 + 64 Combine like terms: -1 + 64 = 63 64 + 16a + a2 = 63 Factor a perfect square on the left side: (a + 8)(a + 8) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (a + 8) equal to 7.937253933 and -7.937253933.Subproblem 1
a + 8 = 7.937253933 Simplifying a + 8 = 7.937253933 Reorder the terms: 8 + a = 7.937253933 Solving 8 + a = 7.937253933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 7.937253933 + -8 Combine like terms: 8 + -8 = 0 0 + a = 7.937253933 + -8 a = 7.937253933 + -8 Combine like terms: 7.937253933 + -8 = -0.062746067 a = -0.062746067 Simplifying a = -0.062746067Subproblem 2
a + 8 = -7.937253933 Simplifying a + 8 = -7.937253933 Reorder the terms: 8 + a = -7.937253933 Solving 8 + a = -7.937253933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = -7.937253933 + -8 Combine like terms: 8 + -8 = 0 0 + a = -7.937253933 + -8 a = -7.937253933 + -8 Combine like terms: -7.937253933 + -8 = -15.937253933 a = -15.937253933 Simplifying a = -15.937253933Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.062746067, -15.937253933}Solution
a = {-0.062746067, -15.937253933}
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