x^2-4x-428=0

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Solution for x^2-4x-428=0 equation: 


Simplifying
x2 + -4x + -428 = 0

Reorder the terms:
-428 + -4x + x2 = 0

Solving
-428 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '428' to each side of the equation.
-428 + -4x + 428 + x2 = 0 + 428

Reorder the terms:
-428 + 428 + -4x + x2 = 0 + 428

Combine like terms: -428 + 428 = 0
0 + -4x + x2 = 0 + 428
-4x + x2 = 0 + 428

Combine like terms: 0 + 428 = 428
-4x + x2 = 428

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 428 + 4

Reorder the terms:
4 + -4x + x2 = 428 + 4

Combine like terms: 428 + 4 = 432
4 + -4x + x2 = 432

Factor a perfect square on the left side:
(x + -2)(x + -2) = 432

Calculate the square root of the right side: 20.784609691

Break this problem into two subproblems by setting 
(x + -2) equal to 20.784609691 and -20.784609691.


Subproblem 1
x + -2 = 20.784609691

Simplifying
x + -2 = 20.784609691

Reorder the terms:
-2 + x = 20.784609691

Solving
-2 + x = 20.784609691

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 20.784609691 + 2

Combine like terms: -2 + 2 = 0
0 + x = 20.784609691 + 2
x = 20.784609691 + 2

Combine like terms: 20.784609691 + 2 = 22.784609691
x = 22.784609691

Simplifying
x = 22.784609691


Subproblem 2
x + -2 = -20.784609691

Simplifying
x + -2 = -20.784609691

Reorder the terms:
-2 + x = -20.784609691

Solving
-2 + x = -20.784609691

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -20.784609691 + 2

Combine like terms: -2 + 2 = 0
0 + x = -20.784609691 + 2
x = -20.784609691 + 2

Combine like terms: -20.784609691 + 2 = -18.784609691
x = -18.784609691

Simplifying
x = -18.784609691


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.784609691, -18.784609691}

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