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Simplifying x2 + 50x + -900 = 0 Reorder the terms: -900 + 50x + x2 = 0 Solving -900 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + 50x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 50x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 50x + x2 = 0 + 900 50x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 50x + x2 = 900 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 = 900 + 625 Reorder the terms: 625 + 50x + x2 = 900 + 625 Combine like terms: 900 + 625 = 1525 625 + 50x + x2 = 1525 Factor a perfect square on the left side: (x + 25)(x + 25) = 1525 Calculate the square root of the right side: 39.05124838 Break this problem into two subproblems by setting (x + 25) equal to 39.05124838 and -39.05124838.Subproblem 1
x + 25 = 39.05124838 Simplifying x + 25 = 39.05124838 Reorder the terms: 25 + x = 39.05124838 Solving 25 + x = 39.05124838 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 = 39.05124838 + -25 Combine like terms: 25 + -25 = 0 0 + x = 39.05124838 + -25 x = 39.05124838 + -25 Combine like terms: 39.05124838 + -25 = 14.05124838 x = 14.05124838 Simplifying x = 14.05124838Subproblem 2
x + 25 = -39.05124838 Simplifying x + 25 = -39.05124838 Reorder the terms: 25 + x = -39.05124838 Solving 25 + x = -39.05124838 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 = -39.05124838 + -25 Combine like terms: 25 + -25 = 0 0 + x = -39.05124838 + -25 x = -39.05124838 + -25 Combine like terms: -39.05124838 + -25 = -64.05124838 x = -64.05124838 Simplifying x = -64.05124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.05124838, -64.05124838}
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