-5x^2+400x-2550=4000

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Solution for -5x^2+400x-2550=4000 equation: 


Simplifying
-5x2 + 400x + -2550 = 4000

Reorder the terms:
-2550 + 400x + -5x2 = 4000

Solving
-2550 + 400x + -5x2 = 4000

Solving for variable 'x'.

Reorder the terms:
-2550 + -4000 + 400x + -5x2 = 4000 + -4000

Combine like terms: -2550 + -4000 = -6550
-6550 + 400x + -5x2 = 4000 + -4000

Combine like terms: 4000 + -4000 = 0
-6550 + 400x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1310 + 80x + -1x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-1310 + 80x + -1x2)' equal to zero and attempt to solve:

Simplifying
-1310 + 80x + -1x2 = 0

Solving
-1310 + 80x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1310 + -80x + x2 = 0

Move the constant term to the right:

Add '-1310' to each side of the equation.
1310 + -80x + -1310 + x2 = 0 + -1310

Reorder the terms:
1310 + -1310 + -80x + x2 = 0 + -1310

Combine like terms: 1310 + -1310 = 0
0 + -80x + x2 = 0 + -1310
-80x + x2 = 0 + -1310

Combine like terms: 0 + -1310 = -1310
-80x + x2 = -1310

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 = -1310 + 1600

Reorder the terms:
1600 + -80x + x2 = -1310 + 1600

Combine like terms: -1310 + 1600 = 290
1600 + -80x + x2 = 290

Factor a perfect square on the left side:
(x + -40)(x + -40) = 290

Calculate the square root of the right side: 17.029386366

Break this problem into two subproblems by setting 
(x + -40) equal to 17.029386366 and -17.029386366.


Subproblem 1
x + -40 = 17.029386366

Simplifying
x + -40 = 17.029386366

Reorder the terms:
-40 + x = 17.029386366

Solving
-40 + x = 17.029386366

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 = 17.029386366 + 40

Combine like terms: -40 + 40 = 0
0 + x = 17.029386366 + 40
x = 17.029386366 + 40

Combine like terms: 17.029386366 + 40 = 57.029386366
x = 57.029386366

Simplifying
x = 57.029386366


Subproblem 2
x + -40 = -17.029386366

Simplifying
x + -40 = -17.029386366

Reorder the terms:
-40 + x = -17.029386366

Solving
-40 + x = -17.029386366

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 = -17.029386366 + 40

Combine like terms: -40 + 40 = 0
0 + x = -17.029386366 + 40
x = -17.029386366 + 40

Combine like terms: -17.029386366 + 40 = 22.970613634
x = 22.970613634

Simplifying
x = 22.970613634


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {57.029386366, 22.970613634}
Solution
x = {57.029386366, 22.970613634}

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