x^2+3x+18x+21=0

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Solution for x^2+3x+18x+21=0 equation: 


Simplifying
x2 + 3x + 18x + 21 = 0

Reorder the terms:
21 + 3x + 18x + x2 = 0

Combine like terms: 3x + 18x = 21x
21 + 21x + x2 = 0

Solving
21 + 21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -21 + 110.25

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

Combine like terms: -21 + 110.25 = 89.25
110.25 + 21x + x2 = 89.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 89.25

Calculate the square root of the right side: 9.447221814

Break this problem into two subproblems by setting 
(x + 10.5) equal to 9.447221814 and -9.447221814.


Subproblem 1
x + 10.5 = 9.447221814

Simplifying
x + 10.5 = 9.447221814

Reorder the terms:
10.5 + x = 9.447221814

Solving
10.5 + x = 9.447221814

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 = 9.447221814 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 9.447221814 + -10.5
x = 9.447221814 + -10.5

Combine like terms: 9.447221814 + -10.5 = -1.052778186
x = -1.052778186

Simplifying
x = -1.052778186


Subproblem 2
x + 10.5 = -9.447221814

Simplifying
x + 10.5 = -9.447221814

Reorder the terms:
10.5 + x = -9.447221814

Solving
10.5 + x = -9.447221814

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 = -9.447221814 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -9.447221814 + -10.5
x = -9.447221814 + -10.5

Combine like terms: -9.447221814 + -10.5 = -19.947221814
x = -19.947221814

Simplifying
x = -19.947221814


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.052778186, -19.947221814}

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