x^2-21x-93=0

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Solution for x^2-21x-93=0 equation: 


Simplifying
x2 + -21x + -93 = 0

Reorder the terms:
-93 + -21x + x2 = 0

Solving
-93 + -21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + -21x + 93 + x2 = 0 + 93

Reorder the terms:
-93 + 93 + -21x + x2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + -21x + x2 = 0 + 93
-21x + x2 = 0 + 93

Combine like terms: 0 + 93 = 93
-21x + x2 = 93

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 = 93 + 110.25

Reorder the terms:
110.25 + -21x + x2 = 93 + 110.25

Combine like terms: 93 + 110.25 = 203.25
110.25 + -21x + x2 = 203.25

Factor a perfect square on the left side:
(x + -10.5)(x + -10.5) = 203.25

Calculate the square root of the right side: 14.256577429

Break this problem into two subproblems by setting 
(x + -10.5) equal to 14.256577429 and -14.256577429.


Subproblem 1
x + -10.5 = 14.256577429

Simplifying
x + -10.5 = 14.256577429

Reorder the terms:
-10.5 + x = 14.256577429

Solving
-10.5 + x = 14.256577429

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 = 14.256577429 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = 14.256577429 + 10.5
x = 14.256577429 + 10.5

Combine like terms: 14.256577429 + 10.5 = 24.756577429
x = 24.756577429

Simplifying
x = 24.756577429


Subproblem 2
x + -10.5 = -14.256577429

Simplifying
x + -10.5 = -14.256577429

Reorder the terms:
-10.5 + x = -14.256577429

Solving
-10.5 + x = -14.256577429

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 = -14.256577429 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + x = -14.256577429 + 10.5
x = -14.256577429 + 10.5

Combine like terms: -14.256577429 + 10.5 = -3.756577429
x = -3.756577429

Simplifying
x = -3.756577429


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.756577429, -3.756577429}

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