x^2+400x-7500=0

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Solution for x^2+400x-7500=0 equation: 


Simplifying
x2 + 400x + -7500 = 0

Reorder the terms:
-7500 + 400x + x2 = 0

Solving
-7500 + 400x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7500' to each side of the equation.
-7500 + 400x + 7500 + x2 = 0 + 7500

Reorder the terms:
-7500 + 7500 + 400x + x2 = 0 + 7500

Combine like terms: -7500 + 7500 = 0
0 + 400x + x2 = 0 + 7500
400x + x2 = 0 + 7500

Combine like terms: 0 + 7500 = 7500
400x + x2 = 7500

The x term is 400x.  Take half its coefficient (200).
Square it (40000) and add it to both sides.

Add '40000' to each side of the equation.
400x + 40000 + x2 = 7500 + 40000

Reorder the terms:
40000 + 400x + x2 = 7500 + 40000

Combine like terms: 7500 + 40000 = 47500
40000 + 400x + x2 = 47500

Factor a perfect square on the left side:
(x + 200)(x + 200) = 47500

Calculate the square root of the right side: 217.944947177

Break this problem into two subproblems by setting 
(x + 200) equal to 217.944947177 and -217.944947177.


Subproblem 1
x + 200 = 217.944947177

Simplifying
x + 200 = 217.944947177

Reorder the terms:
200 + x = 217.944947177

Solving
200 + x = 217.944947177

Solving for variable 'x'.

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

Add '-200' to each side of the equation.
200 + -200 + x = 217.944947177 + -200

Combine like terms: 200 + -200 = 0
0 + x = 217.944947177 + -200
x = 217.944947177 + -200

Combine like terms: 217.944947177 + -200 = 17.944947177
x = 17.944947177

Simplifying
x = 17.944947177


Subproblem 2
x + 200 = -217.944947177

Simplifying
x + 200 = -217.944947177

Reorder the terms:
200 + x = -217.944947177

Solving
200 + x = -217.944947177

Solving for variable 'x'.

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

Add '-200' to each side of the equation.
200 + -200 + x = -217.944947177 + -200

Combine like terms: 200 + -200 = 0
0 + x = -217.944947177 + -200
x = -217.944947177 + -200

Combine like terms: -217.944947177 + -200 = -417.944947177
x = -417.944947177

Simplifying
x = -417.944947177


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.944947177, -417.944947177}

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