x^2-21x-18=0

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Solution for x^2-21x-18=0 equation: 


Simplifying
x2 + -21x + -18 = 0

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

Solving
-18 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -21x + 18 + x2 = 0 + 18

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

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

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

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 = 18 + 110.25

Reorder the terms:
110.25 + -21x + x2 = 18 + 110.25

Combine like terms: 18 + 110.25 = 128.25
110.25 + -21x + x2 = 128.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 128.25

Calculate the square root of the right side: 11.324751653

Break this problem into two subproblems by setting 
(x + -10.5) equal to 11.324751653 and -11.324751653.


Subproblem 1
x + -10.5 = 11.324751653

Simplifying
x + -10.5 = 11.324751653

Reorder the terms:
-10.5 + x = 11.324751653

Solving
-10.5 + x = 11.324751653

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 = 11.324751653 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 11.324751653 + 10.5
x = 11.324751653 + 10.5

Combine like terms: 11.324751653 + 10.5 = 21.824751653
x = 21.824751653

Simplifying
x = 21.824751653


Subproblem 2
x + -10.5 = -11.324751653

Simplifying
x + -10.5 = -11.324751653

Reorder the terms:
-10.5 + x = -11.324751653

Solving
-10.5 + x = -11.324751653

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 = -11.324751653 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -11.324751653 + 10.5
x = -11.324751653 + 10.5

Combine like terms: -11.324751653 + 10.5 = -0.824751653
x = -0.824751653

Simplifying
x = -0.824751653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.824751653, -0.824751653}

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