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Simplifying a2 + 80a + -6400 = 0 Reorder the terms: -6400 + 80a + a2 = 0 Solving -6400 + 80a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '6400' to each side of the equation. -6400 + 80a + 6400 + a2 = 0 + 6400 Reorder the terms: -6400 + 6400 + 80a + a2 = 0 + 6400 Combine like terms: -6400 + 6400 = 0 0 + 80a + a2 = 0 + 6400 80a + a2 = 0 + 6400 Combine like terms: 0 + 6400 = 6400 80a + a2 = 6400 The a term is 80a. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80a + 1600 + a2 = 6400 + 1600 Reorder the terms: 1600 + 80a + a2 = 6400 + 1600 Combine like terms: 6400 + 1600 = 8000 1600 + 80a + a2 = 8000 Factor a perfect square on the left side: (a + 40)(a + 40) = 8000 Calculate the square root of the right side: 89.4427191 Break this problem into two subproblems by setting (a + 40) equal to 89.4427191 and -89.4427191.Subproblem 1
a + 40 = 89.4427191 Simplifying a + 40 = 89.4427191 Reorder the terms: 40 + a = 89.4427191 Solving 40 + a = 89.4427191 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + a = 89.4427191 + -40 Combine like terms: 40 + -40 = 0 0 + a = 89.4427191 + -40 a = 89.4427191 + -40 Combine like terms: 89.4427191 + -40 = 49.4427191 a = 49.4427191 Simplifying a = 49.4427191Subproblem 2
a + 40 = -89.4427191 Simplifying a + 40 = -89.4427191 Reorder the terms: 40 + a = -89.4427191 Solving 40 + a = -89.4427191 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + a = -89.4427191 + -40 Combine like terms: 40 + -40 = 0 0 + a = -89.4427191 + -40 a = -89.4427191 + -40 Combine like terms: -89.4427191 + -40 = -129.4427191 a = -129.4427191 Simplifying a = -129.4427191Solution
The solution to the problem is based on the solutions from the subproblems. a = {49.4427191, -129.4427191}
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