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Simplifying x2 + -50x + 300 = 0 Reorder the terms: 300 + -50x + x2 = 0 Solving 300 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-300' to each side of the equation. 300 + -50x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -50x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -50x + x2 = 0 + -300 -50x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -50x + x2 = -300 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 = -300 + 625 Reorder the terms: 625 + -50x + x2 = -300 + 625 Combine like terms: -300 + 625 = 325 625 + -50x + x2 = 325 Factor a perfect square on the left side: (x + -25)(x + -25) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + -25) equal to 18.027756377 and -18.027756377.Subproblem 1
x + -25 = 18.027756377 Simplifying x + -25 = 18.027756377 Reorder the terms: -25 + x = 18.027756377 Solving -25 + x = 18.027756377 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 = 18.027756377 + 25 Combine like terms: -25 + 25 = 0 0 + x = 18.027756377 + 25 x = 18.027756377 + 25 Combine like terms: 18.027756377 + 25 = 43.027756377 x = 43.027756377 Simplifying x = 43.027756377Subproblem 2
x + -25 = -18.027756377 Simplifying x + -25 = -18.027756377 Reorder the terms: -25 + x = -18.027756377 Solving -25 + x = -18.027756377 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 = -18.027756377 + 25 Combine like terms: -25 + 25 = 0 0 + x = -18.027756377 + 25 x = -18.027756377 + 25 Combine like terms: -18.027756377 + 25 = 6.972243623 x = 6.972243623 Simplifying x = 6.972243623Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.027756377, 6.972243623}
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