x(x+8)=648

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Solution for x(x+8)=648 equation: 


Simplifying
x(x + 8) = 648

Reorder the terms:
x(8 + x) = 648
(8 * x + x * x) = 648
(8x + x2) = 648

Solving
8x + x2 = 648

Solving for variable 'x'.

Reorder the terms:
-648 + 8x + x2 = 648 + -648

Combine like terms: 648 + -648 = 0
-648 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '648' to each side of the equation.
-648 + 8x + 648 + x2 = 0 + 648

Reorder the terms:
-648 + 648 + 8x + x2 = 0 + 648

Combine like terms: -648 + 648 = 0
0 + 8x + x2 = 0 + 648
8x + x2 = 0 + 648

Combine like terms: 0 + 648 = 648
8x + x2 = 648

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 648 + 16

Reorder the terms:
16 + 8x + x2 = 648 + 16

Combine like terms: 648 + 16 = 664
16 + 8x + x2 = 664

Factor a perfect square on the left side:
(x + 4)(x + 4) = 664

Calculate the square root of the right side: 25.768197453

Break this problem into two subproblems by setting 
(x + 4) equal to 25.768197453 and -25.768197453.


Subproblem 1
x + 4 = 25.768197453

Simplifying
x + 4 = 25.768197453

Reorder the terms:
4 + x = 25.768197453

Solving
4 + x = 25.768197453

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 25.768197453 + -4

Combine like terms: 4 + -4 = 0
0 + x = 25.768197453 + -4
x = 25.768197453 + -4

Combine like terms: 25.768197453 + -4 = 21.768197453
x = 21.768197453

Simplifying
x = 21.768197453


Subproblem 2
x + 4 = -25.768197453

Simplifying
x + 4 = -25.768197453

Reorder the terms:
4 + x = -25.768197453

Solving
4 + x = -25.768197453

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -25.768197453 + -4

Combine like terms: 4 + -4 = 0
0 + x = -25.768197453 + -4
x = -25.768197453 + -4

Combine like terms: -25.768197453 + -4 = -29.768197453
x = -29.768197453

Simplifying
x = -29.768197453


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.768197453, -29.768197453}

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