x^2+x-6400=0

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Solution for x^2+x-6400=0 equation:


Simplifying
x2 + x + -6400 = 0

Reorder the terms:
-6400 + x + x2 = 0

Solving
-6400 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6400' to each side of the equation.
-6400 + x + 6400 + x2 = 0 + 6400

Reorder the terms:
-6400 + 6400 + x + x2 = 0 + 6400

Combine like terms: -6400 + 6400 = 0
0 + x + x2 = 0 + 6400
x + x2 = 0 + 6400

Combine like terms: 0 + 6400 = 6400
x + x2 = 6400

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 6400 + 0.25

Reorder the terms:
0.25 + x + x2 = 6400 + 0.25

Combine like terms: 6400 + 0.25 = 6400.25
0.25 + x + x2 = 6400.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 6400.25

Calculate the square root of the right side: 80.001562485

Break this problem into two subproblems by setting 
(x + 0.5) equal to 80.001562485 and -80.001562485.

Subproblem 1

x + 0.5 = 80.001562485 Simplifying x + 0.5 = 80.001562485 Reorder the terms: 0.5 + x = 80.001562485 Solving 0.5 + x = 80.001562485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 80.001562485 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 80.001562485 + -0.5 x = 80.001562485 + -0.5 Combine like terms: 80.001562485 + -0.5 = 79.501562485 x = 79.501562485 Simplifying x = 79.501562485

Subproblem 2

x + 0.5 = -80.001562485 Simplifying x + 0.5 = -80.001562485 Reorder the terms: 0.5 + x = -80.001562485 Solving 0.5 + x = -80.001562485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -80.001562485 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -80.001562485 + -0.5 x = -80.001562485 + -0.5 Combine like terms: -80.001562485 + -0.5 = -80.501562485 x = -80.501562485 Simplifying x = -80.501562485

Solution

The solution to the problem is based on the solutions from the subproblems. x = {79.501562485, -80.501562485}

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