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Simplifying a2 + 160a + 160 = 0 Reorder the terms: 160 + 160a + a2 = 0 Solving 160 + 160a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-160' to each side of the equation. 160 + 160a + -160 + a2 = 0 + -160 Reorder the terms: 160 + -160 + 160a + a2 = 0 + -160 Combine like terms: 160 + -160 = 0 0 + 160a + a2 = 0 + -160 160a + a2 = 0 + -160 Combine like terms: 0 + -160 = -160 160a + a2 = -160 The a term is 160a. Take half its coefficient (80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. 160a + 6400 + a2 = -160 + 6400 Reorder the terms: 6400 + 160a + a2 = -160 + 6400 Combine like terms: -160 + 6400 = 6240 6400 + 160a + a2 = 6240 Factor a perfect square on the left side: (a + 80)(a + 80) = 6240 Calculate the square root of the right side: 78.993670633 Break this problem into two subproblems by setting (a + 80) equal to 78.993670633 and -78.993670633.Subproblem 1
a + 80 = 78.993670633 Simplifying a + 80 = 78.993670633 Reorder the terms: 80 + a = 78.993670633 Solving 80 + a = 78.993670633 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + a = 78.993670633 + -80 Combine like terms: 80 + -80 = 0 0 + a = 78.993670633 + -80 a = 78.993670633 + -80 Combine like terms: 78.993670633 + -80 = -1.006329367 a = -1.006329367 Simplifying a = -1.006329367Subproblem 2
a + 80 = -78.993670633 Simplifying a + 80 = -78.993670633 Reorder the terms: 80 + a = -78.993670633 Solving 80 + a = -78.993670633 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + a = -78.993670633 + -80 Combine like terms: 80 + -80 = 0 0 + a = -78.993670633 + -80 a = -78.993670633 + -80 Combine like terms: -78.993670633 + -80 = -158.993670633 a = -158.993670633 Simplifying a = -158.993670633Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.006329367, -158.993670633}
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