24x^2+29x+4=0

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Solution for 24x^2+29x+4=0 equation: 


Simplifying
24x2 + 29x + 4 = 0

Reorder the terms:
4 + 29x + 24x2 = 0

Solving
4 + 29x + 24x2 = 0

Solving for variable 'x'.

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

Divide each side by '24'.
0.1666666667 + 1.208333333x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 1.208333333x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 1.208333333x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 1.208333333x + x2 = 0 + -0.1666666667
1.208333333x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
1.208333333x + x2 = -0.1666666667

The x term is 1.208333333x.  Take half its coefficient (0.6041666665).
Square it (0.3650173609) and add it to both sides.

Add '0.3650173609' to each side of the equation.
1.208333333x + 0.3650173609 + x2 = -0.1666666667 + 0.3650173609

Reorder the terms:
0.3650173609 + 1.208333333x + x2 = -0.1666666667 + 0.3650173609

Combine like terms: -0.1666666667 + 0.3650173609 = 0.1983506942
0.3650173609 + 1.208333333x + x2 = 0.1983506942

Factor a perfect square on the left side:
(x + 0.6041666665)(x + 0.6041666665) = 0.1983506942

Calculate the square root of the right side: 0.445365798

Break this problem into two subproblems by setting 
(x + 0.6041666665) equal to 0.445365798 and -0.445365798.


Subproblem 1
x + 0.6041666665 = 0.445365798

Simplifying
x + 0.6041666665 = 0.445365798

Reorder the terms:
0.6041666665 + x = 0.445365798

Solving
0.6041666665 + x = 0.445365798

Solving for variable 'x'.

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

Add '-0.6041666665' to each side of the equation.
0.6041666665 + -0.6041666665 + x = 0.445365798 + -0.6041666665

Combine like terms: 0.6041666665 + -0.6041666665 = 0.0000000000
0.0000000000 + x = 0.445365798 + -0.6041666665
x = 0.445365798 + -0.6041666665

Combine like terms: 0.445365798 + -0.6041666665 = -0.1588008685
x = -0.1588008685

Simplifying
x = -0.1588008685


Subproblem 2
x + 0.6041666665 = -0.445365798

Simplifying
x + 0.6041666665 = -0.445365798

Reorder the terms:
0.6041666665 + x = -0.445365798

Solving
0.6041666665 + x = -0.445365798

Solving for variable 'x'.

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

Add '-0.6041666665' to each side of the equation.
0.6041666665 + -0.6041666665 + x = -0.445365798 + -0.6041666665

Combine like terms: 0.6041666665 + -0.6041666665 = 0.0000000000
0.0000000000 + x = -0.445365798 + -0.6041666665
x = -0.445365798 + -0.6041666665

Combine like terms: -0.445365798 + -0.6041666665 = -1.0495324645
x = -1.0495324645

Simplifying
x = -1.0495324645


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1588008685, -1.0495324645}

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