x^2-253x+150=0

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Solution for x^2-253x+150=0 equation: 


Simplifying
x2 + -253x + 150 = 0

Reorder the terms:
150 + -253x + x2 = 0

Solving
150 + -253x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-150' to each side of the equation.
150 + -253x + -150 + x2 = 0 + -150

Reorder the terms:
150 + -150 + -253x + x2 = 0 + -150

Combine like terms: 150 + -150 = 0
0 + -253x + x2 = 0 + -150
-253x + x2 = 0 + -150

Combine like terms: 0 + -150 = -150
-253x + x2 = -150

The x term is -253x.  Take half its coefficient (-126.5).
Square it (16002.25) and add it to both sides.

Add '16002.25' to each side of the equation.
-253x + 16002.25 + x2 = -150 + 16002.25

Reorder the terms:
16002.25 + -253x + x2 = -150 + 16002.25

Combine like terms: -150 + 16002.25 = 15852.25
16002.25 + -253x + x2 = 15852.25

Factor a perfect square on the left side:
(x + -126.5)(x + -126.5) = 15852.25

Calculate the square root of the right side: 125.905718695

Break this problem into two subproblems by setting 
(x + -126.5) equal to 125.905718695 and -125.905718695.


Subproblem 1
x + -126.5 = 125.905718695

Simplifying
x + -126.5 = 125.905718695

Reorder the terms:
-126.5 + x = 125.905718695

Solving
-126.5 + x = 125.905718695

Solving for variable 'x'.

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

Add '126.5' to each side of the equation.
-126.5 + 126.5 + x = 125.905718695 + 126.5

Combine like terms: -126.5 + 126.5 = 0.0
0.0 + x = 125.905718695 + 126.5
x = 125.905718695 + 126.5

Combine like terms: 125.905718695 + 126.5 = 252.405718695
x = 252.405718695

Simplifying
x = 252.405718695


Subproblem 2
x + -126.5 = -125.905718695

Simplifying
x + -126.5 = -125.905718695

Reorder the terms:
-126.5 + x = -125.905718695

Solving
-126.5 + x = -125.905718695

Solving for variable 'x'.

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

Add '126.5' to each side of the equation.
-126.5 + 126.5 + x = -125.905718695 + 126.5

Combine like terms: -126.5 + 126.5 = 0.0
0.0 + x = -125.905718695 + 126.5
x = -125.905718695 + 126.5

Combine like terms: -125.905718695 + 126.5 = 0.594281305
x = 0.594281305

Simplifying
x = 0.594281305


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {252.405718695, 0.594281305}

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