x^2-39x+376=0

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Solution for x^2-39x+376=0 equation: 


Simplifying
x2 + -39x + 376 = 0

Reorder the terms:
376 + -39x + x2 = 0

Solving
376 + -39x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-376' to each side of the equation.
376 + -39x + -376 + x2 = 0 + -376

Reorder the terms:
376 + -376 + -39x + x2 = 0 + -376

Combine like terms: 376 + -376 = 0
0 + -39x + x2 = 0 + -376
-39x + x2 = 0 + -376

Combine like terms: 0 + -376 = -376
-39x + x2 = -376

The x term is -39x.  Take half its coefficient (-19.5).
Square it (380.25) and add it to both sides.

Add '380.25' to each side of the equation.
-39x + 380.25 + x2 = -376 + 380.25

Reorder the terms:
380.25 + -39x + x2 = -376 + 380.25

Combine like terms: -376 + 380.25 = 4.25
380.25 + -39x + x2 = 4.25

Factor a perfect square on the left side:
(x + -19.5)(x + -19.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -19.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + -19.5 = 2.061552813

Simplifying
x + -19.5 = 2.061552813

Reorder the terms:
-19.5 + x = 2.061552813

Solving
-19.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '19.5' to each side of the equation.
-19.5 + 19.5 + x = 2.061552813 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + x = 2.061552813 + 19.5
x = 2.061552813 + 19.5

Combine like terms: 2.061552813 + 19.5 = 21.561552813
x = 21.561552813

Simplifying
x = 21.561552813


Subproblem 2
x + -19.5 = -2.061552813

Simplifying
x + -19.5 = -2.061552813

Reorder the terms:
-19.5 + x = -2.061552813

Solving
-19.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '19.5' to each side of the equation.
-19.5 + 19.5 + x = -2.061552813 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + x = -2.061552813 + 19.5
x = -2.061552813 + 19.5

Combine like terms: -2.061552813 + 19.5 = 17.438447187
x = 17.438447187

Simplifying
x = 17.438447187


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.561552813, 17.438447187}

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