x^2+21x+63=0

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Solution for x^2+21x+63=0 equation: 


Simplifying
x2 + 21x + 63 = 0

Reorder the terms:
63 + 21x + x2 = 0

Solving
63 + 21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-63' to each side of the equation.
63 + 21x + -63 + x2 = 0 + -63

Reorder the terms:
63 + -63 + 21x + x2 = 0 + -63

Combine like terms: 63 + -63 = 0
0 + 21x + x2 = 0 + -63
21x + x2 = 0 + -63

Combine like terms: 0 + -63 = -63
21x + x2 = -63

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -63 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -63 + 110.25

Combine like terms: -63 + 110.25 = 47.25
110.25 + 21x + x2 = 47.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(x + 10.5) equal to 6.873863542 and -6.873863542.


Subproblem 1
x + 10.5 = 6.873863542

Simplifying
x + 10.5 = 6.873863542

Reorder the terms:
10.5 + x = 6.873863542

Solving
10.5 + x = 6.873863542

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 6.873863542 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 6.873863542 + -10.5
x = 6.873863542 + -10.5

Combine like terms: 6.873863542 + -10.5 = -3.626136458
x = -3.626136458

Simplifying
x = -3.626136458


Subproblem 2
x + 10.5 = -6.873863542

Simplifying
x + 10.5 = -6.873863542

Reorder the terms:
10.5 + x = -6.873863542

Solving
10.5 + x = -6.873863542

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -6.873863542 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -6.873863542 + -10.5
x = -6.873863542 + -10.5

Combine like terms: -6.873863542 + -10.5 = -17.373863542
x = -17.373863542

Simplifying
x = -17.373863542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.626136458, -17.373863542}

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