21x^2+21x-23=0

Solution for 21x^2+21x-23=0 equation:

Simplifying
21x2 + 21x + -23 = 0

Reorder the terms:
-23 + 21x + 21x2 = 0

Solving
-23 + 21x + 21x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
21 the coefficient of the squared term: 

Divide each side by '21'.
-1.095238095 + x + x2 = 0

Move the constant term to the right:

Add '1.095238095' to each side of the equation.
-1.095238095 + x + 1.095238095 + x2 = 0 + 1.095238095

Reorder the terms:
-1.095238095 + 1.095238095 + x + x2 = 0 + 1.095238095

Combine like terms: -1.095238095 + 1.095238095 = 0.000000000
0.000000000 + x + x2 = 0 + 1.095238095
x + x2 = 0 + 1.095238095

Combine like terms: 0 + 1.095238095 = 1.095238095
x + x2 = 1.095238095

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 1.095238095 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.095238095 + 0.25

Combine like terms: 1.095238095 + 0.25 = 1.345238095
1.25 + x2 = 1.345238095

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.345238095

Calculate the square root of the right side: 1.159843996

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.159843996 and -1.159843996.

Subproblem 1
x + 0.5 = 1.159843996

Simplifying
x + 0.5 = 1.159843996

Reorder the terms:
0.5 + x = 1.159843996

Solving
0.5 + x = 1.159843996

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.159843996 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.159843996 + -0.5
x = 1.159843996 + -0.5

Combine like terms: 1.159843996 + -0.5 = 0.659843996
x = 0.659843996

Simplifying
x = 0.659843996

Subproblem 2
x + 0.5 = -1.159843996

Simplifying
x + 0.5 = -1.159843996

Reorder the terms:
0.5 + x = -1.159843996

Solving
0.5 + x = -1.159843996

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.159843996 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.159843996 + -0.5
x = -1.159843996 + -0.5

Combine like terms: -1.159843996 + -0.5 = -1.659843996
x = -1.659843996

Simplifying
x = -1.659843996

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.659843996, -1.659843996}