3x^2-4x-21=0

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Solution for 3x^2-4x-21=0 equation: 


Simplifying
3x2 + -4x + -21 = 0

Reorder the terms:
-21 + -4x + 3x2 = 0

Solving
-21 + -4x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-7 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -1.333333333x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -1.333333333x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1.333333333x + x2 = 0 + 7
-1.333333333x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1.333333333x + x2 = 7

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 7 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 7 + 0.4444444442

Combine like terms: 7 + 0.4444444442 = 7.4444444442
0.4444444442 + -1.333333333x + x2 = 7.4444444442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 7.4444444442

Calculate the square root of the right side: 2.728450924

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 2.728450924 and -2.728450924.


Subproblem 1
x + -0.6666666665 = 2.728450924

Simplifying
x + -0.6666666665 = 2.728450924

Reorder the terms:
-0.6666666665 + x = 2.728450924

Solving
-0.6666666665 + x = 2.728450924

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 2.728450924 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 2.728450924 + 0.6666666665
x = 2.728450924 + 0.6666666665

Combine like terms: 2.728450924 + 0.6666666665 = 3.3951175905
x = 3.3951175905

Simplifying
x = 3.3951175905


Subproblem 2
x + -0.6666666665 = -2.728450924

Simplifying
x + -0.6666666665 = -2.728450924

Reorder the terms:
-0.6666666665 + x = -2.728450924

Solving
-0.6666666665 + x = -2.728450924

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -2.728450924 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -2.728450924 + 0.6666666665
x = -2.728450924 + 0.6666666665

Combine like terms: -2.728450924 + 0.6666666665 = -2.0617842575
x = -2.0617842575

Simplifying
x = -2.0617842575


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.3951175905, -2.0617842575}

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