x(x-8)=21

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Solution for x(x-8)=21 equation: 


Simplifying
x(x + -8) = 21

Reorder the terms:
x(-8 + x) = 21
(-8 * x + x * x) = 21
(-8x + x2) = 21

Solving
-8x + x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + -8x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -8x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -8x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -8x + x2 = 0 + 21
-8x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
-8x + x2 = 21

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 = 21 + 16

Reorder the terms:
16 + -8x + x2 = 21 + 16

Combine like terms: 21 + 16 = 37
16 + -8x + x2 = 37

Factor a perfect square on the left side:
(x + -4)(x + -4) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + -4) equal to 6.08276253 and -6.08276253.


Subproblem 1
x + -4 = 6.08276253

Simplifying
x + -4 = 6.08276253

Reorder the terms:
-4 + x = 6.08276253

Solving
-4 + x = 6.08276253

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 = 6.08276253 + 4

Combine like terms: -4 + 4 = 0
0 + x = 6.08276253 + 4
x = 6.08276253 + 4

Combine like terms: 6.08276253 + 4 = 10.08276253
x = 10.08276253

Simplifying
x = 10.08276253


Subproblem 2
x + -4 = -6.08276253

Simplifying
x + -4 = -6.08276253

Reorder the terms:
-4 + x = -6.08276253

Solving
-4 + x = -6.08276253

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 = -6.08276253 + 4

Combine like terms: -4 + 4 = 0
0 + x = -6.08276253 + 4
x = -6.08276253 + 4

Combine like terms: -6.08276253 + 4 = -2.08276253
x = -2.08276253

Simplifying
x = -2.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.08276253, -2.08276253}

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