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Simplifying 5760000 = x(x + 50) Reorder the terms: 5760000 = x(50 + x) 5760000 = (50 * x + x * x) 5760000 = (50x + x2) Solving 5760000 = 50x + x2 Solving for variable 'x'. Reorder the terms: 5760000 + -50x + -1x2 = 50x + -50x + x2 + -1x2 Combine like terms: 50x + -50x = 0 5760000 + -50x + -1x2 = 0 + x2 + -1x2 5760000 + -50x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5760000 + -50x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5760000 + 50x + x2 = 0 Move the constant term to the right: Add '5760000' to each side of the equation. -5760000 + 50x + 5760000 + x2 = 0 + 5760000 Reorder the terms: -5760000 + 5760000 + 50x + x2 = 0 + 5760000 Combine like terms: -5760000 + 5760000 = 0 0 + 50x + x2 = 0 + 5760000 50x + x2 = 0 + 5760000 Combine like terms: 0 + 5760000 = 5760000 50x + x2 = 5760000 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 = 5760000 + 625 Reorder the terms: 625 + 50x + x2 = 5760000 + 625 Combine like terms: 5760000 + 625 = 5760625 625 + 50x + x2 = 5760625 Factor a perfect square on the left side: (x + 25)(x + 25) = 5760625 Calculate the square root of the right side: 2400.130204801 Break this problem into two subproblems by setting (x + 25) equal to 2400.130204801 and -2400.130204801.Subproblem 1
x + 25 = 2400.130204801 Simplifying x + 25 = 2400.130204801 Reorder the terms: 25 + x = 2400.130204801 Solving 25 + x = 2400.130204801 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 = 2400.130204801 + -25 Combine like terms: 25 + -25 = 0 0 + x = 2400.130204801 + -25 x = 2400.130204801 + -25 Combine like terms: 2400.130204801 + -25 = 2375.130204801 x = 2375.130204801 Simplifying x = 2375.130204801Subproblem 2
x + 25 = -2400.130204801 Simplifying x + 25 = -2400.130204801 Reorder the terms: 25 + x = -2400.130204801 Solving 25 + x = -2400.130204801 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 = -2400.130204801 + -25 Combine like terms: 25 + -25 = 0 0 + x = -2400.130204801 + -25 x = -2400.130204801 + -25 Combine like terms: -2400.130204801 + -25 = -2425.130204801 x = -2425.130204801 Simplifying x = -2425.130204801Solution
The solution to the problem is based on the solutions from the subproblems. x = {2375.130204801, -2425.130204801}
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