x^2-4x-420=0

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Solution for x^2-4x-420=0 equation: 


Simplifying
x2 + -4x + -420 = 0

Reorder the terms:
-420 + -4x + x2 = 0

Solving
-420 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '420' to each side of the equation.
-420 + -4x + 420 + x2 = 0 + 420

Reorder the terms:
-420 + 420 + -4x + x2 = 0 + 420

Combine like terms: -420 + 420 = 0
0 + -4x + x2 = 0 + 420
-4x + x2 = 0 + 420

Combine like terms: 0 + 420 = 420
-4x + x2 = 420

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 = 420 + 4

Reorder the terms:
4 + -4x + x2 = 420 + 4

Combine like terms: 420 + 4 = 424
4 + -4x + x2 = 424

Factor a perfect square on the left side:
(x + -2)(x + -2) = 424

Calculate the square root of the right side: 20.591260282

Break this problem into two subproblems by setting 
(x + -2) equal to 20.591260282 and -20.591260282.


Subproblem 1
x + -2 = 20.591260282

Simplifying
x + -2 = 20.591260282

Reorder the terms:
-2 + x = 20.591260282

Solving
-2 + x = 20.591260282

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 = 20.591260282 + 2

Combine like terms: -2 + 2 = 0
0 + x = 20.591260282 + 2
x = 20.591260282 + 2

Combine like terms: 20.591260282 + 2 = 22.591260282
x = 22.591260282

Simplifying
x = 22.591260282


Subproblem 2
x + -2 = -20.591260282

Simplifying
x + -2 = -20.591260282

Reorder the terms:
-2 + x = -20.591260282

Solving
-2 + x = -20.591260282

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 = -20.591260282 + 2

Combine like terms: -2 + 2 = 0
0 + x = -20.591260282 + 2
x = -20.591260282 + 2

Combine like terms: -20.591260282 + 2 = -18.591260282
x = -18.591260282

Simplifying
x = -18.591260282


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.591260282, -18.591260282}

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