21x^2+14x-4=

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Solution for 21x^2+14x-4= equation: 


Simplifying
21x2 + 14x + -4 = 0

Reorder the terms:
-4 + 14x + 21x2 = 0

Solving
-4 + 14x + 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'.
-0.1904761905 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.1904761905' to each side of the equation.
-0.1904761905 + 0.6666666667x + 0.1904761905 + x2 = 0 + 0.1904761905

Reorder the terms:
-0.1904761905 + 0.1904761905 + 0.6666666667x + x2 = 0 + 0.1904761905

Combine like terms: -0.1904761905 + 0.1904761905 = 0.0000000000
0.0000000000 + 0.6666666667x + x2 = 0 + 0.1904761905
0.6666666667x + x2 = 0 + 0.1904761905

Combine like terms: 0 + 0.1904761905 = 0.1904761905
0.6666666667x + x2 = 0.1904761905

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.1904761905 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.1904761905 + 0.1111111112

Combine like terms: 0.1904761905 + 0.1111111112 = 0.3015873017
0.1111111112 + 0.6666666667x + x2 = 0.3015873017

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.3015873017

Calculate the square root of the right side: 0.549169647

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.549169647 and -0.549169647.


Subproblem 1
x + 0.3333333334 = 0.549169647

Simplifying
x + 0.3333333334 = 0.549169647

Reorder the terms:
0.3333333334 + x = 0.549169647

Solving
0.3333333334 + x = 0.549169647

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.549169647 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.549169647 + -0.3333333334
x = 0.549169647 + -0.3333333334

Combine like terms: 0.549169647 + -0.3333333334 = 0.2158363136
x = 0.2158363136

Simplifying
x = 0.2158363136


Subproblem 2
x + 0.3333333334 = -0.549169647

Simplifying
x + 0.3333333334 = -0.549169647

Reorder the terms:
0.3333333334 + x = -0.549169647

Solving
0.3333333334 + x = -0.549169647

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.549169647 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.549169647 + -0.3333333334
x = -0.549169647 + -0.3333333334

Combine like terms: -0.549169647 + -0.3333333334 = -0.8825029804
x = -0.8825029804

Simplifying
x = -0.8825029804


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2158363136, -0.8825029804}

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