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Simplifying 5(a + 16) * a = 4 Reorder the terms: 5(16 + a) * a = 4 Reorder the terms for easier multiplication: 5a(16 + a) = 4 (16 * 5a + a * 5a) = 4 (80a + 5a2) = 4 Solving 80a + 5a2 = 4 Solving for variable 'a'. Reorder the terms: -4 + 80a + 5a2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 80a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 16a + a2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 16a + 0.8 + a2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 16a + a2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 16a + a2 = 0 + 0.8 16a + a2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 16a + a2 = 0.8 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 = 0.8 + 64 Reorder the terms: 64 + 16a + a2 = 0.8 + 64 Combine like terms: 0.8 + 64 = 64.8 64 + 16a + a2 = 64.8 Factor a perfect square on the left side: (a + 8)(a + 8) = 64.8 Calculate the square root of the right side: 8.049844719 Break this problem into two subproblems by setting (a + 8) equal to 8.049844719 and -8.049844719.Subproblem 1
a + 8 = 8.049844719 Simplifying a + 8 = 8.049844719 Reorder the terms: 8 + a = 8.049844719 Solving 8 + a = 8.049844719 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 = 8.049844719 + -8 Combine like terms: 8 + -8 = 0 0 + a = 8.049844719 + -8 a = 8.049844719 + -8 Combine like terms: 8.049844719 + -8 = 0.049844719 a = 0.049844719 Simplifying a = 0.049844719Subproblem 2
a + 8 = -8.049844719 Simplifying a + 8 = -8.049844719 Reorder the terms: 8 + a = -8.049844719 Solving 8 + a = -8.049844719 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 = -8.049844719 + -8 Combine like terms: 8 + -8 = 0 0 + a = -8.049844719 + -8 a = -8.049844719 + -8 Combine like terms: -8.049844719 + -8 = -16.049844719 a = -16.049844719 Simplifying a = -16.049844719Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.049844719, -16.049844719}
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