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Simplifying x2 + -50x + -100 = 0 Reorder the terms: -100 + -50x + x2 = 0 Solving -100 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -50x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -50x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -50x + x2 = 0 + 100 -50x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -50x + x2 = 100 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 = 100 + 625 Reorder the terms: 625 + -50x + x2 = 100 + 625 Combine like terms: 100 + 625 = 725 625 + -50x + x2 = 725 Factor a perfect square on the left side: (x + -25)(x + -25) = 725 Calculate the square root of the right side: 26.925824036 Break this problem into two subproblems by setting (x + -25) equal to 26.925824036 and -26.925824036.Subproblem 1
x + -25 = 26.925824036 Simplifying x + -25 = 26.925824036 Reorder the terms: -25 + x = 26.925824036 Solving -25 + x = 26.925824036 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 = 26.925824036 + 25 Combine like terms: -25 + 25 = 0 0 + x = 26.925824036 + 25 x = 26.925824036 + 25 Combine like terms: 26.925824036 + 25 = 51.925824036 x = 51.925824036 Simplifying x = 51.925824036Subproblem 2
x + -25 = -26.925824036 Simplifying x + -25 = -26.925824036 Reorder the terms: -25 + x = -26.925824036 Solving -25 + x = -26.925824036 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 = -26.925824036 + 25 Combine like terms: -25 + 25 = 0 0 + x = -26.925824036 + 25 x = -26.925824036 + 25 Combine like terms: -26.925824036 + 25 = -1.925824036 x = -1.925824036 Simplifying x = -1.925824036Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.925824036, -1.925824036}
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