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Simplifying x2 = 1000 + 50x Solving x2 = 1000 + 50x Solving for variable 'x'. Reorder the terms: -1000 + -50x + x2 = 1000 + 50x + -1000 + -50x Reorder the terms: -1000 + -50x + x2 = 1000 + -1000 + 50x + -50x Combine like terms: 1000 + -1000 = 0 -1000 + -50x + x2 = 0 + 50x + -50x -1000 + -50x + x2 = 50x + -50x Combine like terms: 50x + -50x = 0 -1000 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -50x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -50x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -50x + x2 = 0 + 1000 -50x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -50x + x2 = 1000 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 = 1000 + 625 Reorder the terms: 625 + -50x + x2 = 1000 + 625 Combine like terms: 1000 + 625 = 1625 625 + -50x + x2 = 1625 Factor a perfect square on the left side: (x + -25)(x + -25) = 1625 Calculate the square root of the right side: 40.311288741 Break this problem into two subproblems by setting (x + -25) equal to 40.311288741 and -40.311288741.Subproblem 1
x + -25 = 40.311288741 Simplifying x + -25 = 40.311288741 Reorder the terms: -25 + x = 40.311288741 Solving -25 + x = 40.311288741 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 = 40.311288741 + 25 Combine like terms: -25 + 25 = 0 0 + x = 40.311288741 + 25 x = 40.311288741 + 25 Combine like terms: 40.311288741 + 25 = 65.311288741 x = 65.311288741 Simplifying x = 65.311288741Subproblem 2
x + -25 = -40.311288741 Simplifying x + -25 = -40.311288741 Reorder the terms: -25 + x = -40.311288741 Solving -25 + x = -40.311288741 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 = -40.311288741 + 25 Combine like terms: -25 + 25 = 0 0 + x = -40.311288741 + 25 x = -40.311288741 + 25 Combine like terms: -40.311288741 + 25 = -15.311288741 x = -15.311288741 Simplifying x = -15.311288741Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.311288741, -15.311288741}
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