5x^2-400x-6750=0

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Solution for 5x^2-400x-6750=0 equation: 


Simplifying
5x2 + -400x + -6750 = 0

Reorder the terms:
-6750 + -400x + 5x2 = 0

Solving
-6750 + -400x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1350 + -80x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-1350 + -80x + x2)' equal to zero and attempt to solve:

Simplifying
-1350 + -80x + x2 = 0

Solving
-1350 + -80x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1350' to each side of the equation.
-1350 + -80x + 1350 + x2 = 0 + 1350

Reorder the terms:
-1350 + 1350 + -80x + x2 = 0 + 1350

Combine like terms: -1350 + 1350 = 0
0 + -80x + x2 = 0 + 1350
-80x + x2 = 0 + 1350

Combine like terms: 0 + 1350 = 1350
-80x + x2 = 1350

The x term is -80x.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80x + 1600 + x2 = 1350 + 1600

Reorder the terms:
1600 + -80x + x2 = 1350 + 1600

Combine like terms: 1350 + 1600 = 2950
1600 + -80x + x2 = 2950

Factor a perfect square on the left side:
(x + -40)(x + -40) = 2950

Calculate the square root of the right side: 54.313902456

Break this problem into two subproblems by setting 
(x + -40) equal to 54.313902456 and -54.313902456.


Subproblem 1
x + -40 = 54.313902456

Simplifying
x + -40 = 54.313902456

Reorder the terms:
-40 + x = 54.313902456

Solving
-40 + x = 54.313902456

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = 54.313902456 + 40

Combine like terms: -40 + 40 = 0
0 + x = 54.313902456 + 40
x = 54.313902456 + 40

Combine like terms: 54.313902456 + 40 = 94.313902456
x = 94.313902456

Simplifying
x = 94.313902456


Subproblem 2
x + -40 = -54.313902456

Simplifying
x + -40 = -54.313902456

Reorder the terms:
-40 + x = -54.313902456

Solving
-40 + x = -54.313902456

Solving for variable 'x'.

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

Add '40' to each side of the equation.
-40 + 40 + x = -54.313902456 + 40

Combine like terms: -40 + 40 = 0
0 + x = -54.313902456 + 40
x = -54.313902456 + 40

Combine like terms: -54.313902456 + 40 = -14.313902456
x = -14.313902456

Simplifying
x = -14.313902456


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {94.313902456, -14.313902456}
Solution
x = {94.313902456, -14.313902456}

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