x^2+100x-4000=0

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Solution for x^2+100x-4000=0 equation:


Simplifying
x2 + 100x + -4000 = 0

Reorder the terms:
-4000 + 100x + x2 = 0

Solving
-4000 + 100x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4000' to each side of the equation.
-4000 + 100x + 4000 + x2 = 0 + 4000

Reorder the terms:
-4000 + 4000 + 100x + x2 = 0 + 4000

Combine like terms: -4000 + 4000 = 0
0 + 100x + x2 = 0 + 4000
100x + x2 = 0 + 4000

Combine like terms: 0 + 4000 = 4000
100x + x2 = 4000

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 = 4000 + 2500

Reorder the terms:
2500 + 100x + x2 = 4000 + 2500

Combine like terms: 4000 + 2500 = 6500
2500 + 100x + x2 = 6500

Factor a perfect square on the left side:
(x + 50)(x + 50) = 6500

Calculate the square root of the right side: 80.622577483

Break this problem into two subproblems by setting 
(x + 50) equal to 80.622577483 and -80.622577483.

Subproblem 1

x + 50 = 80.622577483 Simplifying x + 50 = 80.622577483 Reorder the terms: 50 + x = 80.622577483 Solving 50 + x = 80.622577483 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 = 80.622577483 + -50 Combine like terms: 50 + -50 = 0 0 + x = 80.622577483 + -50 x = 80.622577483 + -50 Combine like terms: 80.622577483 + -50 = 30.622577483 x = 30.622577483 Simplifying x = 30.622577483

Subproblem 2

x + 50 = -80.622577483 Simplifying x + 50 = -80.622577483 Reorder the terms: 50 + x = -80.622577483 Solving 50 + x = -80.622577483 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 = -80.622577483 + -50 Combine like terms: 50 + -50 = 0 0 + x = -80.622577483 + -50 x = -80.622577483 + -50 Combine like terms: -80.622577483 + -50 = -130.622577483 x = -130.622577483 Simplifying x = -130.622577483

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.622577483, -130.622577483}

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