(x+8)(x-2)-21=0

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Solution for (x+8)(x-2)-21=0 equation: 


Simplifying
(x + 8)(x + -2) + -21 = 0

Reorder the terms:
(8 + x)(x + -2) + -21 = 0

Reorder the terms:
(8 + x)(-2 + x) + -21 = 0

Multiply (8 + x) * (-2 + x)
(8(-2 + x) + x(-2 + x)) + -21 = 0
((-2 * 8 + x * 8) + x(-2 + x)) + -21 = 0
((-16 + 8x) + x(-2 + x)) + -21 = 0
(-16 + 8x + (-2 * x + x * x)) + -21 = 0
(-16 + 8x + (-2x + x2)) + -21 = 0

Combine like terms: 8x + -2x = 6x
(-16 + 6x + x2) + -21 = 0

Reorder the terms:
-16 + -21 + 6x + x2 = 0

Combine like terms: -16 + -21 = -37
-37 + 6x + x2 = 0

Solving
-37 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 6x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + 6x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 6x + x2 = 0 + 37
6x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
6x + x2 = 37

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 = 37 + 9

Reorder the terms:
9 + 6x + x2 = 37 + 9

Combine like terms: 37 + 9 = 46
9 + 6x + x2 = 46

Factor a perfect square on the left side:
(x + 3)(x + 3) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 3) equal to 6.782329983 and -6.782329983.


Subproblem 1
x + 3 = 6.782329983

Simplifying
x + 3 = 6.782329983

Reorder the terms:
3 + x = 6.782329983

Solving
3 + x = 6.782329983

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 = 6.782329983 + -3

Combine like terms: 3 + -3 = 0
0 + x = 6.782329983 + -3
x = 6.782329983 + -3

Combine like terms: 6.782329983 + -3 = 3.782329983
x = 3.782329983

Simplifying
x = 3.782329983


Subproblem 2
x + 3 = -6.782329983

Simplifying
x + 3 = -6.782329983

Reorder the terms:
3 + x = -6.782329983

Solving
3 + x = -6.782329983

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 = -6.782329983 + -3

Combine like terms: 3 + -3 = 0
0 + x = -6.782329983 + -3
x = -6.782329983 + -3

Combine like terms: -6.782329983 + -3 = -9.782329983
x = -9.782329983

Simplifying
x = -9.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.782329983, -9.782329983}

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