x^2-30x-44000=0

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Solution for x^2-30x-44000=0 equation: 


Simplifying
x2 + -30x + -44000 = 0

Reorder the terms:
-44000 + -30x + x2 = 0

Solving
-44000 + -30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '44000' to each side of the equation.
-44000 + -30x + 44000 + x2 = 0 + 44000

Reorder the terms:
-44000 + 44000 + -30x + x2 = 0 + 44000

Combine like terms: -44000 + 44000 = 0
0 + -30x + x2 = 0 + 44000
-30x + x2 = 0 + 44000

Combine like terms: 0 + 44000 = 44000
-30x + x2 = 44000

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 44000 + 225

Reorder the terms:
225 + -30x + x2 = 44000 + 225

Combine like terms: 44000 + 225 = 44225
225 + -30x + x2 = 44225

Factor a perfect square on the left side:
(x + -15)(x + -15) = 44225

Calculate the square root of the right side: 210.297408448

Break this problem into two subproblems by setting 
(x + -15) equal to 210.297408448 and -210.297408448.


Subproblem 1
x + -15 = 210.297408448

Simplifying
x + -15 = 210.297408448

Reorder the terms:
-15 + x = 210.297408448

Solving
-15 + x = 210.297408448

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 210.297408448 + 15

Combine like terms: -15 + 15 = 0
0 + x = 210.297408448 + 15
x = 210.297408448 + 15

Combine like terms: 210.297408448 + 15 = 225.297408448
x = 225.297408448

Simplifying
x = 225.297408448


Subproblem 2
x + -15 = -210.297408448

Simplifying
x + -15 = -210.297408448

Reorder the terms:
-15 + x = -210.297408448

Solving
-15 + x = -210.297408448

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -210.297408448 + 15

Combine like terms: -15 + 15 = 0
0 + x = -210.297408448 + 15
x = -210.297408448 + 15

Combine like terms: -210.297408448 + 15 = -195.297408448
x = -195.297408448

Simplifying
x = -195.297408448


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {225.297408448, -195.297408448}

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