x^2+21x-66=0

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Solution for x^2+21x-66=0 equation:


Simplifying
x2 + 21x + -66 = 0

Reorder the terms:
-66 + 21x + x2 = 0

Solving
-66 + 21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 21x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + 21x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 21x + x2 = 0 + 66
21x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
21x + x2 = 66

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 = 66 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 66 + 110.25

Combine like terms: 66 + 110.25 = 176.25
110.25 + 21x + x2 = 176.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 176.25

Calculate the square root of the right side: 13.275918047

Break this problem into two subproblems by setting 
(x + 10.5) equal to 13.275918047 and -13.275918047.


Subproblem 1
x + 10.5 = 13.275918047

Simplifying
x + 10.5 = 13.275918047

Reorder the terms:
10.5 + x = 13.275918047

Solving
10.5 + x = 13.275918047

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 = 13.275918047 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 13.275918047 + -10.5
x = 13.275918047 + -10.5

Combine like terms: 13.275918047 + -10.5 = 2.775918047
x = 2.775918047

Simplifying
x = 2.775918047


Subproblem 2
x + 10.5 = -13.275918047

Simplifying
x + 10.5 = -13.275918047

Reorder the terms:
10.5 + x = -13.275918047

Solving
10.5 + x = -13.275918047

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 = -13.275918047 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -13.275918047 + -10.5
x = -13.275918047 + -10.5

Combine like terms: -13.275918047 + -10.5 = -23.775918047
x = -23.775918047

Simplifying
x = -23.775918047


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.775918047, -23.775918047}

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