2.1x^2+10.5x-6=0

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Solution for 2.1x^2+10.5x-6=0 equation: 


Simplifying
2.1x2 + 10.5x + -6 = 0

Reorder the terms:
-6 + 10.5x + 2.1x2 = 0

Solving
-6 + 10.5x + 2.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.1'.
-2.857142857 + 5x + x2 = 0

Move the constant term to the right:

Add '2.857142857' to each side of the equation.
-2.857142857 + 5x + 2.857142857 + x2 = 0 + 2.857142857

Reorder the terms:
-2.857142857 + 2.857142857 + 5x + x2 = 0 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + 5x + x2 = 0 + 2.857142857
5x + x2 = 0 + 2.857142857

Combine like terms: 0 + 2.857142857 = 2.857142857
5x + x2 = 2.857142857

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2.857142857 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2.857142857 + 6.25

Combine like terms: 2.857142857 + 6.25 = 9.107142857
6.25 + 5x + x2 = 9.107142857

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 9.107142857

Calculate the square root of the right side: 3.017804311

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.017804311 and -3.017804311.


Subproblem 1
x + 2.5 = 3.017804311

Simplifying
x + 2.5 = 3.017804311

Reorder the terms:
2.5 + x = 3.017804311

Solving
2.5 + x = 3.017804311

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.017804311 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.017804311 + -2.5
x = 3.017804311 + -2.5

Combine like terms: 3.017804311 + -2.5 = 0.517804311
x = 0.517804311

Simplifying
x = 0.517804311


Subproblem 2
x + 2.5 = -3.017804311

Simplifying
x + 2.5 = -3.017804311

Reorder the terms:
2.5 + x = -3.017804311

Solving
2.5 + x = -3.017804311

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.017804311 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.017804311 + -2.5
x = -3.017804311 + -2.5

Combine like terms: -3.017804311 + -2.5 = -5.517804311
x = -5.517804311

Simplifying
x = -5.517804311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.517804311, -5.517804311}

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