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Simplifying x2 + -50x = 125 Reorder the terms: -50x + x2 = 125 Solving -50x + x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + -50x + x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + -50x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -50x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -50x + x2 = 0 + 125 -50x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -50x + x2 = 125 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 = 125 + 625 Reorder the terms: 625 + -50x + x2 = 125 + 625 Combine like terms: 125 + 625 = 750 625 + -50x + x2 = 750 Factor a perfect square on the left side: (x + -25)(x + -25) = 750 Calculate the square root of the right side: 27.386127875 Break this problem into two subproblems by setting (x + -25) equal to 27.386127875 and -27.386127875.Subproblem 1
x + -25 = 27.386127875 Simplifying x + -25 = 27.386127875 Reorder the terms: -25 + x = 27.386127875 Solving -25 + x = 27.386127875 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 = 27.386127875 + 25 Combine like terms: -25 + 25 = 0 0 + x = 27.386127875 + 25 x = 27.386127875 + 25 Combine like terms: 27.386127875 + 25 = 52.386127875 x = 52.386127875 Simplifying x = 52.386127875Subproblem 2
x + -25 = -27.386127875 Simplifying x + -25 = -27.386127875 Reorder the terms: -25 + x = -27.386127875 Solving -25 + x = -27.386127875 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 = -27.386127875 + 25 Combine like terms: -25 + 25 = 0 0 + x = -27.386127875 + 25 x = -27.386127875 + 25 Combine like terms: -27.386127875 + 25 = -2.386127875 x = -2.386127875 Simplifying x = -2.386127875Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.386127875, -2.386127875}
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