21.4x^2-16.4x-12.4=0

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Solution for 21.4x^2-16.4x-12.4=0 equation: 


Simplifying
21.4x2 + -16.4x + -12.4 = 0

Reorder the terms:
-12.4 + -16.4x + 21.4x2 = 0

Solving
-12.4 + -16.4x + 21.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '21.4'.
-0.5794392523 + -0.7663551402x + x2 = 0

Move the constant term to the right:

Add '0.5794392523' to each side of the equation.
-0.5794392523 + -0.7663551402x + 0.5794392523 + x2 = 0 + 0.5794392523

Reorder the terms:
-0.5794392523 + 0.5794392523 + -0.7663551402x + x2 = 0 + 0.5794392523

Combine like terms: -0.5794392523 + 0.5794392523 = 0.0000000000
0.0000000000 + -0.7663551402x + x2 = 0 + 0.5794392523
-0.7663551402x + x2 = 0 + 0.5794392523

Combine like terms: 0 + 0.5794392523 = 0.5794392523
-0.7663551402x + x2 = 0.5794392523

The x term is -0.7663551402x.  Take half its coefficient (-0.3831775701).
Square it (0.1468250502) and add it to both sides.

Add '0.1468250502' to each side of the equation.
-0.7663551402x + 0.1468250502 + x2 = 0.5794392523 + 0.1468250502

Reorder the terms:
0.1468250502 + -0.7663551402x + x2 = 0.5794392523 + 0.1468250502

Combine like terms: 0.5794392523 + 0.1468250502 = 0.7262643025
0.1468250502 + -0.7663551402x + x2 = 0.7262643025

Factor a perfect square on the left side:
(x + -0.3831775701)(x + -0.3831775701) = 0.7262643025

Calculate the square root of the right side: 0.852211419

Break this problem into two subproblems by setting 
(x + -0.3831775701) equal to 0.852211419 and -0.852211419.


Subproblem 1
x + -0.3831775701 = 0.852211419

Simplifying
x + -0.3831775701 = 0.852211419

Reorder the terms:
-0.3831775701 + x = 0.852211419

Solving
-0.3831775701 + x = 0.852211419

Solving for variable 'x'.

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

Add '0.3831775701' to each side of the equation.
-0.3831775701 + 0.3831775701 + x = 0.852211419 + 0.3831775701

Combine like terms: -0.3831775701 + 0.3831775701 = 0.0000000000
0.0000000000 + x = 0.852211419 + 0.3831775701
x = 0.852211419 + 0.3831775701

Combine like terms: 0.852211419 + 0.3831775701 = 1.2353889891
x = 1.2353889891

Simplifying
x = 1.2353889891


Subproblem 2
x + -0.3831775701 = -0.852211419

Simplifying
x + -0.3831775701 = -0.852211419

Reorder the terms:
-0.3831775701 + x = -0.852211419

Solving
-0.3831775701 + x = -0.852211419

Solving for variable 'x'.

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

Add '0.3831775701' to each side of the equation.
-0.3831775701 + 0.3831775701 + x = -0.852211419 + 0.3831775701

Combine like terms: -0.3831775701 + 0.3831775701 = 0.0000000000
0.0000000000 + x = -0.852211419 + 0.3831775701
x = -0.852211419 + 0.3831775701

Combine like terms: -0.852211419 + 0.3831775701 = -0.4690338489
x = -0.4690338489

Simplifying
x = -0.4690338489


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2353889891, -0.4690338489}

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