x^2-100x+2500=1250

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Solution for x^2-100x+2500=1250 equation:


Simplifying
x2 + -100x + 2500 = 1250

Reorder the terms:
2500 + -100x + x2 = 1250

Solving
2500 + -100x + x2 = 1250

Solving for variable 'x'.

Reorder the terms:
2500 + -1250 + -100x + x2 = 1250 + -1250

Combine like terms: 2500 + -1250 = 1250
1250 + -100x + x2 = 1250 + -1250

Combine like terms: 1250 + -1250 = 0
1250 + -100x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1250' to each side of the equation.
1250 + -100x + -1250 + x2 = 0 + -1250

Reorder the terms:
1250 + -1250 + -100x + x2 = 0 + -1250

Combine like terms: 1250 + -1250 = 0
0 + -100x + x2 = 0 + -1250
-100x + x2 = 0 + -1250

Combine like terms: 0 + -1250 = -1250
-100x + x2 = -1250

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = -1250 + 2500

Reorder the terms:
2500 + -100x + x2 = -1250 + 2500

Combine like terms: -1250 + 2500 = 1250
2500 + -100x + x2 = 1250

Factor a perfect square on the left side:
(x + -50)(x + -50) = 1250

Calculate the square root of the right side: 35.355339059

Break this problem into two subproblems by setting 
(x + -50) equal to 35.355339059 and -35.355339059.

Subproblem 1

x + -50 = 35.355339059 Simplifying x + -50 = 35.355339059 Reorder the terms: -50 + x = 35.355339059 Solving -50 + x = 35.355339059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 35.355339059 + 50 Combine like terms: -50 + 50 = 0 0 + x = 35.355339059 + 50 x = 35.355339059 + 50 Combine like terms: 35.355339059 + 50 = 85.355339059 x = 85.355339059 Simplifying x = 85.355339059

Subproblem 2

x + -50 = -35.355339059 Simplifying x + -50 = -35.355339059 Reorder the terms: -50 + x = -35.355339059 Solving -50 + x = -35.355339059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -35.355339059 + 50 Combine like terms: -50 + 50 = 0 0 + x = -35.355339059 + 50 x = -35.355339059 + 50 Combine like terms: -35.355339059 + 50 = 14.644660941 x = 14.644660941 Simplifying x = 14.644660941

Solution

The solution to the problem is based on the solutions from the subproblems. x = {85.355339059, 14.644660941}

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