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Simplifying x2 + 50x + -600 = 760 Reorder the terms: -600 + 50x + x2 = 760 Solving -600 + 50x + x2 = 760 Solving for variable 'x'. Reorder the terms: -600 + -760 + 50x + x2 = 760 + -760 Combine like terms: -600 + -760 = -1360 -1360 + 50x + x2 = 760 + -760 Combine like terms: 760 + -760 = 0 -1360 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1360' to each side of the equation. -1360 + 50x + 1360 + x2 = 0 + 1360 Reorder the terms: -1360 + 1360 + 50x + x2 = 0 + 1360 Combine like terms: -1360 + 1360 = 0 0 + 50x + x2 = 0 + 1360 50x + x2 = 0 + 1360 Combine like terms: 0 + 1360 = 1360 50x + x2 = 1360 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 = 1360 + 625 Reorder the terms: 625 + 50x + x2 = 1360 + 625 Combine like terms: 1360 + 625 = 1985 625 + 50x + x2 = 1985 Factor a perfect square on the left side: (x + 25)(x + 25) = 1985 Calculate the square root of the right side: 44.55333882 Break this problem into two subproblems by setting (x + 25) equal to 44.55333882 and -44.55333882.Subproblem 1
x + 25 = 44.55333882 Simplifying x + 25 = 44.55333882 Reorder the terms: 25 + x = 44.55333882 Solving 25 + x = 44.55333882 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 = 44.55333882 + -25 Combine like terms: 25 + -25 = 0 0 + x = 44.55333882 + -25 x = 44.55333882 + -25 Combine like terms: 44.55333882 + -25 = 19.55333882 x = 19.55333882 Simplifying x = 19.55333882Subproblem 2
x + 25 = -44.55333882 Simplifying x + 25 = -44.55333882 Reorder the terms: 25 + x = -44.55333882 Solving 25 + x = -44.55333882 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 = -44.55333882 + -25 Combine like terms: 25 + -25 = 0 0 + x = -44.55333882 + -25 x = -44.55333882 + -25 Combine like terms: -44.55333882 + -25 = -69.55333882 x = -69.55333882 Simplifying x = -69.55333882Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.55333882, -69.55333882}
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