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Simplifying x2 + 50x + -5400 = 0 Reorder the terms: -5400 + 50x + x2 = 0 Solving -5400 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5400' to each side of the equation. -5400 + 50x + 5400 + x2 = 0 + 5400 Reorder the terms: -5400 + 5400 + 50x + x2 = 0 + 5400 Combine like terms: -5400 + 5400 = 0 0 + 50x + x2 = 0 + 5400 50x + x2 = 0 + 5400 Combine like terms: 0 + 5400 = 5400 50x + x2 = 5400 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 5400 + 625 Reorder the terms: 625 + 50x + x2 = 5400 + 625 Combine like terms: 5400 + 625 = 6025 625 + 50x + x2 = 6025 Factor a perfect square on the left side: (x + 25)(x + 25) = 6025 Calculate the square root of the right side: 77.620873481 Break this problem into two subproblems by setting (x + 25) equal to 77.620873481 and -77.620873481.Subproblem 1
x + 25 = 77.620873481 Simplifying x + 25 = 77.620873481 Reorder the terms: 25 + x = 77.620873481 Solving 25 + x = 77.620873481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 77.620873481 + -25 Combine like terms: 25 + -25 = 0 0 + x = 77.620873481 + -25 x = 77.620873481 + -25 Combine like terms: 77.620873481 + -25 = 52.620873481 x = 52.620873481 Simplifying x = 52.620873481Subproblem 2
x + 25 = -77.620873481 Simplifying x + 25 = -77.620873481 Reorder the terms: 25 + x = -77.620873481 Solving 25 + x = -77.620873481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -77.620873481 + -25 Combine like terms: 25 + -25 = 0 0 + x = -77.620873481 + -25 x = -77.620873481 + -25 Combine like terms: -77.620873481 + -25 = -102.620873481 x = -102.620873481 Simplifying x = -102.620873481Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.620873481, -102.620873481}
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