x^2-150x+2000=0

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Solution for x^2-150x+2000=0 equation: 


Simplifying
x2 + -150x + 2000 = 0

Reorder the terms:
2000 + -150x + x2 = 0

Solving
2000 + -150x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2000' to each side of the equation.
2000 + -150x + -2000 + x2 = 0 + -2000

Reorder the terms:
2000 + -2000 + -150x + x2 = 0 + -2000

Combine like terms: 2000 + -2000 = 0
0 + -150x + x2 = 0 + -2000
-150x + x2 = 0 + -2000

Combine like terms: 0 + -2000 = -2000
-150x + x2 = -2000

The x term is -150x.  Take half its coefficient (-75).
Square it (5625) and add it to both sides.

Add '5625' to each side of the equation.
-150x + 5625 + x2 = -2000 + 5625

Reorder the terms:
5625 + -150x + x2 = -2000 + 5625

Combine like terms: -2000 + 5625 = 3625
5625 + -150x + x2 = 3625

Factor a perfect square on the left side:
(x + -75)(x + -75) = 3625

Calculate the square root of the right side: 60.207972894

Break this problem into two subproblems by setting 
(x + -75) equal to 60.207972894 and -60.207972894.


Subproblem 1
x + -75 = 60.207972894

Simplifying
x + -75 = 60.207972894

Reorder the terms:
-75 + x = 60.207972894

Solving
-75 + x = 60.207972894

Solving for variable 'x'.

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

Add '75' to each side of the equation.
-75 + 75 + x = 60.207972894 + 75

Combine like terms: -75 + 75 = 0
0 + x = 60.207972894 + 75
x = 60.207972894 + 75

Combine like terms: 60.207972894 + 75 = 135.207972894
x = 135.207972894

Simplifying
x = 135.207972894


Subproblem 2
x + -75 = -60.207972894

Simplifying
x + -75 = -60.207972894

Reorder the terms:
-75 + x = -60.207972894

Solving
-75 + x = -60.207972894

Solving for variable 'x'.

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

Add '75' to each side of the equation.
-75 + 75 + x = -60.207972894 + 75

Combine like terms: -75 + 75 = 0
0 + x = -60.207972894 + 75
x = -60.207972894 + 75

Combine like terms: -60.207972894 + 75 = 14.792027106
x = 14.792027106

Simplifying
x = 14.792027106


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {135.207972894, 14.792027106}

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