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Simplifying x2 + -50x + 168 = 0 Reorder the terms: 168 + -50x + x2 = 0 Solving 168 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-168' to each side of the equation. 168 + -50x + -168 + x2 = 0 + -168 Reorder the terms: 168 + -168 + -50x + x2 = 0 + -168 Combine like terms: 168 + -168 = 0 0 + -50x + x2 = 0 + -168 -50x + x2 = 0 + -168 Combine like terms: 0 + -168 = -168 -50x + x2 = -168 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 = -168 + 625 Reorder the terms: 625 + -50x + x2 = -168 + 625 Combine like terms: -168 + 625 = 457 625 + -50x + x2 = 457 Factor a perfect square on the left side: (x + -25)(x + -25) = 457 Calculate the square root of the right side: 21.377558326 Break this problem into two subproblems by setting (x + -25) equal to 21.377558326 and -21.377558326.Subproblem 1
x + -25 = 21.377558326 Simplifying x + -25 = 21.377558326 Reorder the terms: -25 + x = 21.377558326 Solving -25 + x = 21.377558326 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 = 21.377558326 + 25 Combine like terms: -25 + 25 = 0 0 + x = 21.377558326 + 25 x = 21.377558326 + 25 Combine like terms: 21.377558326 + 25 = 46.377558326 x = 46.377558326 Simplifying x = 46.377558326Subproblem 2
x + -25 = -21.377558326 Simplifying x + -25 = -21.377558326 Reorder the terms: -25 + x = -21.377558326 Solving -25 + x = -21.377558326 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 = -21.377558326 + 25 Combine like terms: -25 + 25 = 0 0 + x = -21.377558326 + 25 x = -21.377558326 + 25 Combine like terms: -21.377558326 + 25 = 3.622441674 x = 3.622441674 Simplifying x = 3.622441674Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.377558326, 3.622441674}
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