x^2-50x+125=0

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Solution for x^2-50x+125=0 equation:


Simplifying
x2 + -50x + 125 = 0

Reorder the terms:
125 + -50x + x2 = 0

Solving
125 + -50x + x2 = 0

Solving for variable 'x'.

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 = 500
625 + -50x + x2 = 500

Factor a perfect square on the left side:
(x + -25)(x + -25) = 500

Calculate the square root of the right side: 22.360679775

Break this problem into two subproblems by setting 
(x + -25) equal to 22.360679775 and -22.360679775.

Subproblem 1

x + -25 = 22.360679775 Simplifying x + -25 = 22.360679775 Reorder the terms: -25 + x = 22.360679775 Solving -25 + x = 22.360679775 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 = 22.360679775 + 25 Combine like terms: -25 + 25 = 0 0 + x = 22.360679775 + 25 x = 22.360679775 + 25 Combine like terms: 22.360679775 + 25 = 47.360679775 x = 47.360679775 Simplifying x = 47.360679775

Subproblem 2

x + -25 = -22.360679775 Simplifying x + -25 = -22.360679775 Reorder the terms: -25 + x = -22.360679775 Solving -25 + x = -22.360679775 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 = -22.360679775 + 25 Combine like terms: -25 + 25 = 0 0 + x = -22.360679775 + 25 x = -22.360679775 + 25 Combine like terms: -22.360679775 + 25 = 2.639320225 x = 2.639320225 Simplifying x = 2.639320225

Solution

The solution to the problem is based on the solutions from the subproblems. x = {47.360679775, 2.639320225}

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