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Simplifying a2 + -160a + -800 = 0 Reorder the terms: -800 + -160a + a2 = 0 Solving -800 + -160a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + -160a + 800 + a2 = 0 + 800 Reorder the terms: -800 + 800 + -160a + a2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + -160a + a2 = 0 + 800 -160a + a2 = 0 + 800 Combine like terms: 0 + 800 = 800 -160a + a2 = 800 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 = 800 + 6400 Reorder the terms: 6400 + -160a + a2 = 800 + 6400 Combine like terms: 800 + 6400 = 7200 6400 + -160a + a2 = 7200 Factor a perfect square on the left side: (a + -80)(a + -80) = 7200 Calculate the square root of the right side: 84.852813742 Break this problem into two subproblems by setting (a + -80) equal to 84.852813742 and -84.852813742.Subproblem 1
a + -80 = 84.852813742 Simplifying a + -80 = 84.852813742 Reorder the terms: -80 + a = 84.852813742 Solving -80 + a = 84.852813742 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 = 84.852813742 + 80 Combine like terms: -80 + 80 = 0 0 + a = 84.852813742 + 80 a = 84.852813742 + 80 Combine like terms: 84.852813742 + 80 = 164.852813742 a = 164.852813742 Simplifying a = 164.852813742Subproblem 2
a + -80 = -84.852813742 Simplifying a + -80 = -84.852813742 Reorder the terms: -80 + a = -84.852813742 Solving -80 + a = -84.852813742 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 = -84.852813742 + 80 Combine like terms: -80 + 80 = 0 0 + a = -84.852813742 + 80 a = -84.852813742 + 80 Combine like terms: -84.852813742 + 80 = -4.852813742 a = -4.852813742 Simplifying a = -4.852813742Solution
The solution to the problem is based on the solutions from the subproblems. a = {164.852813742, -4.852813742}
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