3x^2+20x-4=0

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Solution for 3x^2+20x-4=0 equation: 


Simplifying
3x2 + 20x + -4 = 0

Reorder the terms:
-4 + 20x + 3x2 = 0

Solving
-4 + 20x + 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'.
-1.333333333 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 6.666666667x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 6.666666667x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 6.666666667x + x2 = 0 + 1.333333333
6.666666667x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
6.666666667x + x2 = 1.333333333

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 1.333333333 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 1.333333333 + 11.11111112

Combine like terms: 1.333333333 + 11.11111112 = 12.444444453
11.11111112 + 6.666666667x + x2 = 12.444444453

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 12.444444453

Calculate the square root of the right side: 3.527668416

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 3.527668416 and -3.527668416.


Subproblem 1
x + 3.333333334 = 3.527668416

Simplifying
x + 3.333333334 = 3.527668416

Reorder the terms:
3.333333334 + x = 3.527668416

Solving
3.333333334 + x = 3.527668416

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 3.527668416 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 3.527668416 + -3.333333334
x = 3.527668416 + -3.333333334

Combine like terms: 3.527668416 + -3.333333334 = 0.194335082
x = 0.194335082

Simplifying
x = 0.194335082


Subproblem 2
x + 3.333333334 = -3.527668416

Simplifying
x + 3.333333334 = -3.527668416

Reorder the terms:
3.333333334 + x = -3.527668416

Solving
3.333333334 + x = -3.527668416

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -3.527668416 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -3.527668416 + -3.333333334
x = -3.527668416 + -3.333333334

Combine like terms: -3.527668416 + -3.333333334 = -6.86100175
x = -6.86100175

Simplifying
x = -6.86100175


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.194335082, -6.86100175}

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