x^2-100x-2500=0

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Solution for x^2-100x-2500=0 equation:


Simplifying
x2 + -100x + -2500 = 0

Reorder the terms:
-2500 + -100x + x2 = 0

Solving
-2500 + -100x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2500' to each side of the equation.
-2500 + -100x + 2500 + x2 = 0 + 2500

Reorder the terms:
-2500 + 2500 + -100x + x2 = 0 + 2500

Combine like terms: -2500 + 2500 = 0
0 + -100x + x2 = 0 + 2500
-100x + x2 = 0 + 2500

Combine like terms: 0 + 2500 = 2500
-100x + x2 = 2500

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 = 2500 + 2500

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

Combine like terms: 2500 + 2500 = 5000
2500 + -100x + x2 = 5000

Factor a perfect square on the left side:
(x + -50)(x + -50) = 5000

Calculate the square root of the right side: 70.710678119

Break this problem into two subproblems by setting 
(x + -50) equal to 70.710678119 and -70.710678119.

Subproblem 1

x + -50 = 70.710678119 Simplifying x + -50 = 70.710678119 Reorder the terms: -50 + x = 70.710678119 Solving -50 + x = 70.710678119 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 = 70.710678119 + 50 Combine like terms: -50 + 50 = 0 0 + x = 70.710678119 + 50 x = 70.710678119 + 50 Combine like terms: 70.710678119 + 50 = 120.710678119 x = 120.710678119 Simplifying x = 120.710678119

Subproblem 2

x + -50 = -70.710678119 Simplifying x + -50 = -70.710678119 Reorder the terms: -50 + x = -70.710678119 Solving -50 + x = -70.710678119 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 = -70.710678119 + 50 Combine like terms: -50 + 50 = 0 0 + x = -70.710678119 + 50 x = -70.710678119 + 50 Combine like terms: -70.710678119 + 50 = -20.710678119 x = -20.710678119 Simplifying x = -20.710678119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {120.710678119, -20.710678119}

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