2.1x^2+10x-16=0

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Solution for 2.1x^2+10x-16=0 equation: 


Simplifying
2.1x2 + 10x + -16 = 0

Reorder the terms:
-16 + 10x + 2.1x2 = 0

Solving
-16 + 10x + 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'.
-7.619047619 + 4.761904762x + x2 = 0

Move the constant term to the right:

Add '7.619047619' to each side of the equation.
-7.619047619 + 4.761904762x + 7.619047619 + x2 = 0 + 7.619047619

Reorder the terms:
-7.619047619 + 7.619047619 + 4.761904762x + x2 = 0 + 7.619047619

Combine like terms: -7.619047619 + 7.619047619 = 0.000000000
0.000000000 + 4.761904762x + x2 = 0 + 7.619047619
4.761904762x + x2 = 0 + 7.619047619

Combine like terms: 0 + 7.619047619 = 7.619047619
4.761904762x + x2 = 7.619047619

The x term is 4.761904762x.  Take half its coefficient (2.380952381).
Square it (5.668934241) and add it to both sides.

Add '5.668934241' to each side of the equation.
4.761904762x + 5.668934241 + x2 = 7.619047619 + 5.668934241

Reorder the terms:
5.668934241 + 4.761904762x + x2 = 7.619047619 + 5.668934241

Combine like terms: 7.619047619 + 5.668934241 = 13.28798186
5.668934241 + 4.761904762x + x2 = 13.28798186

Factor a perfect square on the left side:
(x + 2.380952381)(x + 2.380952381) = 13.28798186

Calculate the square root of the right side: 3.645268421

Break this problem into two subproblems by setting 
(x + 2.380952381) equal to 3.645268421 and -3.645268421.


Subproblem 1
x + 2.380952381 = 3.645268421

Simplifying
x + 2.380952381 = 3.645268421

Reorder the terms:
2.380952381 + x = 3.645268421

Solving
2.380952381 + x = 3.645268421

Solving for variable 'x'.

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

Add '-2.380952381' to each side of the equation.
2.380952381 + -2.380952381 + x = 3.645268421 + -2.380952381

Combine like terms: 2.380952381 + -2.380952381 = 0.000000000
0.000000000 + x = 3.645268421 + -2.380952381
x = 3.645268421 + -2.380952381

Combine like terms: 3.645268421 + -2.380952381 = 1.26431604
x = 1.26431604

Simplifying
x = 1.26431604


Subproblem 2
x + 2.380952381 = -3.645268421

Simplifying
x + 2.380952381 = -3.645268421

Reorder the terms:
2.380952381 + x = -3.645268421

Solving
2.380952381 + x = -3.645268421

Solving for variable 'x'.

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

Add '-2.380952381' to each side of the equation.
2.380952381 + -2.380952381 + x = -3.645268421 + -2.380952381

Combine like terms: 2.380952381 + -2.380952381 = 0.000000000
0.000000000 + x = -3.645268421 + -2.380952381
x = -3.645268421 + -2.380952381

Combine like terms: -3.645268421 + -2.380952381 = -6.026220802
x = -6.026220802

Simplifying
x = -6.026220802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.26431604, -6.026220802}

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