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Simplifying x2 + 160x + 375 = 0 Reorder the terms: 375 + 160x + x2 = 0 Solving 375 + 160x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-375' to each side of the equation. 375 + 160x + -375 + x2 = 0 + -375 Reorder the terms: 375 + -375 + 160x + x2 = 0 + -375 Combine like terms: 375 + -375 = 0 0 + 160x + x2 = 0 + -375 160x + x2 = 0 + -375 Combine like terms: 0 + -375 = -375 160x + x2 = -375 The x term is 160x. Take half its coefficient (80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. 160x + 6400 + x2 = -375 + 6400 Reorder the terms: 6400 + 160x + x2 = -375 + 6400 Combine like terms: -375 + 6400 = 6025 6400 + 160x + x2 = 6025 Factor a perfect square on the left side: (x + 80)(x + 80) = 6025 Calculate the square root of the right side: 77.620873481 Break this problem into two subproblems by setting (x + 80) equal to 77.620873481 and -77.620873481.Subproblem 1
x + 80 = 77.620873481 Simplifying x + 80 = 77.620873481 Reorder the terms: 80 + x = 77.620873481 Solving 80 + x = 77.620873481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = 77.620873481 + -80 Combine like terms: 80 + -80 = 0 0 + x = 77.620873481 + -80 x = 77.620873481 + -80 Combine like terms: 77.620873481 + -80 = -2.379126519 x = -2.379126519 Simplifying x = -2.379126519Subproblem 2
x + 80 = -77.620873481 Simplifying x + 80 = -77.620873481 Reorder the terms: 80 + x = -77.620873481 Solving 80 + x = -77.620873481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = -77.620873481 + -80 Combine like terms: 80 + -80 = 0 0 + x = -77.620873481 + -80 x = -77.620873481 + -80 Combine like terms: -77.620873481 + -80 = -157.620873481 x = -157.620873481 Simplifying x = -157.620873481Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.379126519, -157.620873481}
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