(x-3)(x-3)=21

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Solution for (x-3)(x-3)=21 equation: 


Simplifying
(x + -3)(x + -3) = 21

Reorder the terms:
(-3 + x)(x + -3) = 21

Reorder the terms:
(-3 + x)(-3 + x) = 21

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) = 21
((-3 * -3 + x * -3) + x(-3 + x)) = 21
((9 + -3x) + x(-3 + x)) = 21
(9 + -3x + (-3 * x + x * x)) = 21
(9 + -3x + (-3x + x2)) = 21

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) = 21

Solving
9 + -6x + x2 = 21

Solving for variable 'x'.

Reorder the terms:
9 + -21 + -6x + x2 = 21 + -21

Combine like terms: 9 + -21 = -12
-12 + -6x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-12 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -6x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -6x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -6x + x2 = 0 + 12
-6x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-6x + x2 = 12

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 12 + 9

Reorder the terms:
9 + -6x + x2 = 12 + 9

Combine like terms: 12 + 9 = 21
9 + -6x + x2 = 21

Factor a perfect square on the left side:
(x + -3)(x + -3) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -3) equal to 4.582575695 and -4.582575695.


Subproblem 1
x + -3 = 4.582575695

Simplifying
x + -3 = 4.582575695

Reorder the terms:
-3 + x = 4.582575695

Solving
-3 + x = 4.582575695

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 4.582575695 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.582575695 + 3
x = 4.582575695 + 3

Combine like terms: 4.582575695 + 3 = 7.582575695
x = 7.582575695

Simplifying
x = 7.582575695


Subproblem 2
x + -3 = -4.582575695

Simplifying
x + -3 = -4.582575695

Reorder the terms:
-3 + x = -4.582575695

Solving
-3 + x = -4.582575695

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -4.582575695 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.582575695 + 3
x = -4.582575695 + 3

Combine like terms: -4.582575695 + 3 = -1.582575695
x = -1.582575695

Simplifying
x = -1.582575695


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.582575695, -1.582575695}

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