x^2-62x+313=0

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Solution for x^2-62x+313=0 equation: 


Simplifying
x2 + -62x + 313 = 0

Reorder the terms:
313 + -62x + x2 = 0

Solving
313 + -62x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-313' to each side of the equation.
313 + -62x + -313 + x2 = 0 + -313

Reorder the terms:
313 + -313 + -62x + x2 = 0 + -313

Combine like terms: 313 + -313 = 0
0 + -62x + x2 = 0 + -313
-62x + x2 = 0 + -313

Combine like terms: 0 + -313 = -313
-62x + x2 = -313

The x term is -62x.  Take half its coefficient (-31).
Square it (961) and add it to both sides.

Add '961' to each side of the equation.
-62x + 961 + x2 = -313 + 961

Reorder the terms:
961 + -62x + x2 = -313 + 961

Combine like terms: -313 + 961 = 648
961 + -62x + x2 = 648

Factor a perfect square on the left side:
(x + -31)(x + -31) = 648

Calculate the square root of the right side: 25.455844123

Break this problem into two subproblems by setting 
(x + -31) equal to 25.455844123 and -25.455844123.


Subproblem 1
x + -31 = 25.455844123

Simplifying
x + -31 = 25.455844123

Reorder the terms:
-31 + x = 25.455844123

Solving
-31 + x = 25.455844123

Solving for variable 'x'.

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

Add '31' to each side of the equation.
-31 + 31 + x = 25.455844123 + 31

Combine like terms: -31 + 31 = 0
0 + x = 25.455844123 + 31
x = 25.455844123 + 31

Combine like terms: 25.455844123 + 31 = 56.455844123
x = 56.455844123

Simplifying
x = 56.455844123


Subproblem 2
x + -31 = -25.455844123

Simplifying
x + -31 = -25.455844123

Reorder the terms:
-31 + x = -25.455844123

Solving
-31 + x = -25.455844123

Solving for variable 'x'.

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

Add '31' to each side of the equation.
-31 + 31 + x = -25.455844123 + 31

Combine like terms: -31 + 31 = 0
0 + x = -25.455844123 + 31
x = -25.455844123 + 31

Combine like terms: -25.455844123 + 31 = 5.544155877
x = 5.544155877

Simplifying
x = 5.544155877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {56.455844123, 5.544155877}

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