x(x-8)=38

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Solution for x(x-8)=38 equation: 


Simplifying
x(x + -8) = 38

Reorder the terms:
x(-8 + x) = 38
(-8 * x + x * x) = 38
(-8x + x2) = 38

Solving
-8x + x2 = 38

Solving for variable 'x'.

Reorder the terms:
-38 + -8x + x2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + -8x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + -8x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + -8x + x2 = 0 + 38
-8x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
-8x + x2 = 38

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 = 38 + 16

Reorder the terms:
16 + -8x + x2 = 38 + 16

Combine like terms: 38 + 16 = 54
16 + -8x + x2 = 54

Factor a perfect square on the left side:
(x + -4)(x + -4) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + -4) equal to 7.348469228 and -7.348469228.


Subproblem 1
x + -4 = 7.348469228

Simplifying
x + -4 = 7.348469228

Reorder the terms:
-4 + x = 7.348469228

Solving
-4 + x = 7.348469228

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 = 7.348469228 + 4

Combine like terms: -4 + 4 = 0
0 + x = 7.348469228 + 4
x = 7.348469228 + 4

Combine like terms: 7.348469228 + 4 = 11.348469228
x = 11.348469228

Simplifying
x = 11.348469228


Subproblem 2
x + -4 = -7.348469228

Simplifying
x + -4 = -7.348469228

Reorder the terms:
-4 + x = -7.348469228

Solving
-4 + x = -7.348469228

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 = -7.348469228 + 4

Combine like terms: -4 + 4 = 0
0 + x = -7.348469228 + 4
x = -7.348469228 + 4

Combine like terms: -7.348469228 + 4 = -3.348469228
x = -3.348469228

Simplifying
x = -3.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.348469228, -3.348469228}

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