x^2-21x-216=0

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Solution for x^2-21x-216=0 equation: 


Simplifying
x2 + -21x + -216 = 0

Reorder the terms:
-216 + -21x + x2 = 0

Solving
-216 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '216' to each side of the equation.
-216 + -21x + 216 + x2 = 0 + 216

Reorder the terms:
-216 + 216 + -21x + x2 = 0 + 216

Combine like terms: -216 + 216 = 0
0 + -21x + x2 = 0 + 216
-21x + x2 = 0 + 216

Combine like terms: 0 + 216 = 216
-21x + x2 = 216

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 = 216 + 110.25

Reorder the terms:
110.25 + -21x + x2 = 216 + 110.25

Combine like terms: 216 + 110.25 = 326.25
110.25 + -21x + x2 = 326.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 326.25

Calculate the square root of the right side: 18.062391868

Break this problem into two subproblems by setting 
(x + -10.5) equal to 18.062391868 and -18.062391868.


Subproblem 1
x + -10.5 = 18.062391868

Simplifying
x + -10.5 = 18.062391868

Reorder the terms:
-10.5 + x = 18.062391868

Solving
-10.5 + x = 18.062391868

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 = 18.062391868 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 18.062391868 + 10.5
x = 18.062391868 + 10.5

Combine like terms: 18.062391868 + 10.5 = 28.562391868
x = 28.562391868

Simplifying
x = 28.562391868


Subproblem 2
x + -10.5 = -18.062391868

Simplifying
x + -10.5 = -18.062391868

Reorder the terms:
-10.5 + x = -18.062391868

Solving
-10.5 + x = -18.062391868

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 = -18.062391868 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -18.062391868 + 10.5
x = -18.062391868 + 10.5

Combine like terms: -18.062391868 + 10.5 = -7.562391868
x = -7.562391868

Simplifying
x = -7.562391868


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.562391868, -7.562391868}

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