x^2+5x-400=0

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Solution for x^2+5x-400=0 equation: 


Simplifying
x2 + 5x + -400 = 0

Reorder the terms:
-400 + 5x + x2 = 0

Solving
-400 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + 5x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + 5x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + 5x + x2 = 0 + 400
5x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
5x + x2 = 400

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 400 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 400 + 6.25

Combine like terms: 400 + 6.25 = 406.25
6.25 + 5x + x2 = 406.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 406.25

Calculate the square root of the right side: 20.155644371

Break this problem into two subproblems by setting 
(x + 2.5) equal to 20.155644371 and -20.155644371.


Subproblem 1
x + 2.5 = 20.155644371

Simplifying
x + 2.5 = 20.155644371

Reorder the terms:
2.5 + x = 20.155644371

Solving
2.5 + x = 20.155644371

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 20.155644371 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 20.155644371 + -2.5
x = 20.155644371 + -2.5

Combine like terms: 20.155644371 + -2.5 = 17.655644371
x = 17.655644371

Simplifying
x = 17.655644371


Subproblem 2
x + 2.5 = -20.155644371

Simplifying
x + 2.5 = -20.155644371

Reorder the terms:
2.5 + x = -20.155644371

Solving
2.5 + x = -20.155644371

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -20.155644371 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -20.155644371 + -2.5
x = -20.155644371 + -2.5

Combine like terms: -20.155644371 + -2.5 = -22.655644371
x = -22.655644371

Simplifying
x = -22.655644371


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.655644371, -22.655644371}

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