3x^2+29x+4=0

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Solution for 3x^2+29x+4=0 equation: 


Simplifying
3x2 + 29x + 4 = 0

Reorder the terms:
4 + 29x + 3x2 = 0

Solving
4 + 29x + 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 + 9.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 9.666666667x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 9.666666667x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 9.666666667x + x2 = 0 + -1.333333333
9.666666667x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
9.666666667x + x2 = -1.333333333

The x term is 9.666666667x.  Take half its coefficient (4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
9.666666667x + 23.36111112 + x2 = -1.333333333 + 23.36111112

Reorder the terms:
23.36111112 + 9.666666667x + x2 = -1.333333333 + 23.36111112

Combine like terms: -1.333333333 + 23.36111112 = 22.027777787
23.36111112 + 9.666666667x + x2 = 22.027777787

Factor a perfect square on the left side:
(x + 4.833333334)(x + 4.833333334) = 22.027777787

Calculate the square root of the right side: 4.693375948

Break this problem into two subproblems by setting 
(x + 4.833333334) equal to 4.693375948 and -4.693375948.


Subproblem 1
x + 4.833333334 = 4.693375948

Simplifying
x + 4.833333334 = 4.693375948

Reorder the terms:
4.833333334 + x = 4.693375948

Solving
4.833333334 + x = 4.693375948

Solving for variable 'x'.

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

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + x = 4.693375948 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + x = 4.693375948 + -4.833333334
x = 4.693375948 + -4.833333334

Combine like terms: 4.693375948 + -4.833333334 = -0.139957386
x = -0.139957386

Simplifying
x = -0.139957386


Subproblem 2
x + 4.833333334 = -4.693375948

Simplifying
x + 4.833333334 = -4.693375948

Reorder the terms:
4.833333334 + x = -4.693375948

Solving
4.833333334 + x = -4.693375948

Solving for variable 'x'.

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

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + x = -4.693375948 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + x = -4.693375948 + -4.833333334
x = -4.693375948 + -4.833333334

Combine like terms: -4.693375948 + -4.833333334 = -9.526709282
x = -9.526709282

Simplifying
x = -9.526709282


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.139957386, -9.526709282}

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