x*x-5x=1000

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Solution for x*x-5x=1000 equation: 


Simplifying
x * x + -5x = 1000

Multiply x * x
x2 + -5x = 1000

Reorder the terms:
-5x + x2 = 1000

Solving
-5x + x2 = 1000

Solving for variable 'x'.

Reorder the terms:
-1000 + -5x + x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-1000 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + -5x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + -5x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + -5x + x2 = 0 + 1000
-5x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
-5x + x2 = 1000

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 = 1000 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 1000 + 6.25

Combine like terms: 1000 + 6.25 = 1006.25
6.25 + -5x + x2 = 1006.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1006.25

Calculate the square root of the right side: 31.721443851

Break this problem into two subproblems by setting 
(x + -2.5) equal to 31.721443851 and -31.721443851.


Subproblem 1
x + -2.5 = 31.721443851

Simplifying
x + -2.5 = 31.721443851

Reorder the terms:
-2.5 + x = 31.721443851

Solving
-2.5 + x = 31.721443851

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 = 31.721443851 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 31.721443851 + 2.5
x = 31.721443851 + 2.5

Combine like terms: 31.721443851 + 2.5 = 34.221443851
x = 34.221443851

Simplifying
x = 34.221443851


Subproblem 2
x + -2.5 = -31.721443851

Simplifying
x + -2.5 = -31.721443851

Reorder the terms:
-2.5 + x = -31.721443851

Solving
-2.5 + x = -31.721443851

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 = -31.721443851 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -31.721443851 + 2.5
x = -31.721443851 + 2.5

Combine like terms: -31.721443851 + 2.5 = -29.221443851
x = -29.221443851

Simplifying
x = -29.221443851


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.221443851, -29.221443851}

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