4x^2-158x+854=0

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Solution for 4x^2-158x+854=0 equation: 


Simplifying
4x2 + -158x + 854 = 0

Reorder the terms:
854 + -158x + 4x2 = 0

Solving
854 + -158x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(427 + -79x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(427 + -79x + 2x2)' equal to zero and attempt to solve:

Simplifying
427 + -79x + 2x2 = 0

Solving
427 + -79x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
213.5 + -39.5x + x2 = 0

Move the constant term to the right:

Add '-213.5' to each side of the equation.
213.5 + -39.5x + -213.5 + x2 = 0 + -213.5

Reorder the terms:
213.5 + -213.5 + -39.5x + x2 = 0 + -213.5

Combine like terms: 213.5 + -213.5 = 0.0
0.0 + -39.5x + x2 = 0 + -213.5
-39.5x + x2 = 0 + -213.5

Combine like terms: 0 + -213.5 = -213.5
-39.5x + x2 = -213.5

The x term is -39.5x.  Take half its coefficient (-19.75).
Square it (390.0625) and add it to both sides.

Add '390.0625' to each side of the equation.
-39.5x + 390.0625 + x2 = -213.5 + 390.0625

Reorder the terms:
390.0625 + -39.5x + x2 = -213.5 + 390.0625

Combine like terms: -213.5 + 390.0625 = 176.5625
390.0625 + -39.5x + x2 = 176.5625

Factor a perfect square on the left side:
(x + -19.75)(x + -19.75) = 176.5625

Calculate the square root of the right side: 13.287682266

Break this problem into two subproblems by setting 
(x + -19.75) equal to 13.287682266 and -13.287682266.


Subproblem 1
x + -19.75 = 13.287682266

Simplifying
x + -19.75 = 13.287682266

Reorder the terms:
-19.75 + x = 13.287682266

Solving
-19.75 + x = 13.287682266

Solving for variable 'x'.

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

Add '19.75' to each side of the equation.
-19.75 + 19.75 + x = 13.287682266 + 19.75

Combine like terms: -19.75 + 19.75 = 0.00
0.00 + x = 13.287682266 + 19.75
x = 13.287682266 + 19.75

Combine like terms: 13.287682266 + 19.75 = 33.037682266
x = 33.037682266

Simplifying
x = 33.037682266


Subproblem 2
x + -19.75 = -13.287682266

Simplifying
x + -19.75 = -13.287682266

Reorder the terms:
-19.75 + x = -13.287682266

Solving
-19.75 + x = -13.287682266

Solving for variable 'x'.

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

Add '19.75' to each side of the equation.
-19.75 + 19.75 + x = -13.287682266 + 19.75

Combine like terms: -19.75 + 19.75 = 0.00
0.00 + x = -13.287682266 + 19.75
x = -13.287682266 + 19.75

Combine like terms: -13.287682266 + 19.75 = 6.462317734
x = 6.462317734

Simplifying
x = 6.462317734


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.037682266, 6.462317734}
Solution
x = {33.037682266, 6.462317734}

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