x^2-550x+126=0

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Solution for x^2-550x+126=0 equation: 


Simplifying
x2 + -550x + 126 = 0

Reorder the terms:
126 + -550x + x2 = 0

Solving
126 + -550x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-126' to each side of the equation.
126 + -550x + -126 + x2 = 0 + -126

Reorder the terms:
126 + -126 + -550x + x2 = 0 + -126

Combine like terms: 126 + -126 = 0
0 + -550x + x2 = 0 + -126
-550x + x2 = 0 + -126

Combine like terms: 0 + -126 = -126
-550x + x2 = -126

The x term is -550x.  Take half its coefficient (-275).
Square it (75625) and add it to both sides.

Add '75625' to each side of the equation.
-550x + 75625 + x2 = -126 + 75625

Reorder the terms:
75625 + -550x + x2 = -126 + 75625

Combine like terms: -126 + 75625 = 75499
75625 + -550x + x2 = 75499

Factor a perfect square on the left side:
(x + -275)(x + -275) = 75499

Calculate the square root of the right side: 274.770813588

Break this problem into two subproblems by setting 
(x + -275) equal to 274.770813588 and -274.770813588.


Subproblem 1
x + -275 = 274.770813588

Simplifying
x + -275 = 274.770813588

Reorder the terms:
-275 + x = 274.770813588

Solving
-275 + x = 274.770813588

Solving for variable 'x'.

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

Add '275' to each side of the equation.
-275 + 275 + x = 274.770813588 + 275

Combine like terms: -275 + 275 = 0
0 + x = 274.770813588 + 275
x = 274.770813588 + 275

Combine like terms: 274.770813588 + 275 = 549.770813588
x = 549.770813588

Simplifying
x = 549.770813588


Subproblem 2
x + -275 = -274.770813588

Simplifying
x + -275 = -274.770813588

Reorder the terms:
-275 + x = -274.770813588

Solving
-275 + x = -274.770813588

Solving for variable 'x'.

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

Add '275' to each side of the equation.
-275 + 275 + x = -274.770813588 + 275

Combine like terms: -275 + 275 = 0
0 + x = -274.770813588 + 275
x = -274.770813588 + 275

Combine like terms: -274.770813588 + 275 = 0.229186412
x = 0.229186412

Simplifying
x = 0.229186412


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {549.770813588, 0.229186412}

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