x(x-4)=448

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Solution for x(x-4)=448 equation: 


Simplifying
x(x + -4) = 448

Reorder the terms:
x(-4 + x) = 448
(-4 * x + x * x) = 448
(-4x + x2) = 448

Solving
-4x + x2 = 448

Solving for variable 'x'.

Reorder the terms:
-448 + -4x + x2 = 448 + -448

Combine like terms: 448 + -448 = 0
-448 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '448' to each side of the equation.
-448 + -4x + 448 + x2 = 0 + 448

Reorder the terms:
-448 + 448 + -4x + x2 = 0 + 448

Combine like terms: -448 + 448 = 0
0 + -4x + x2 = 0 + 448
-4x + x2 = 0 + 448

Combine like terms: 0 + 448 = 448
-4x + x2 = 448

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 = 448 + 4

Reorder the terms:
4 + -4x + x2 = 448 + 4

Combine like terms: 448 + 4 = 452
4 + -4x + x2 = 452

Factor a perfect square on the left side:
(x + -2)(x + -2) = 452

Calculate the square root of the right side: 21.260291625

Break this problem into two subproblems by setting 
(x + -2) equal to 21.260291625 and -21.260291625.


Subproblem 1
x + -2 = 21.260291625

Simplifying
x + -2 = 21.260291625

Reorder the terms:
-2 + x = 21.260291625

Solving
-2 + x = 21.260291625

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 = 21.260291625 + 2

Combine like terms: -2 + 2 = 0
0 + x = 21.260291625 + 2
x = 21.260291625 + 2

Combine like terms: 21.260291625 + 2 = 23.260291625
x = 23.260291625

Simplifying
x = 23.260291625


Subproblem 2
x + -2 = -21.260291625

Simplifying
x + -2 = -21.260291625

Reorder the terms:
-2 + x = -21.260291625

Solving
-2 + x = -21.260291625

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 = -21.260291625 + 2

Combine like terms: -2 + 2 = 0
0 + x = -21.260291625 + 2
x = -21.260291625 + 2

Combine like terms: -21.260291625 + 2 = -19.260291625
x = -19.260291625

Simplifying
x = -19.260291625


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.260291625, -19.260291625}

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