24x^2+84x+29=0

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Solution for 24x^2+84x+29=0 equation: 


Simplifying
24x2 + 84x + 29 = 0

Reorder the terms:
29 + 84x + 24x2 = 0

Solving
29 + 84x + 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'.
1.208333333 + 3.5x + x2 = 0

Move the constant term to the right:

Add '-1.208333333' to each side of the equation.
1.208333333 + 3.5x + -1.208333333 + x2 = 0 + -1.208333333

Reorder the terms:
1.208333333 + -1.208333333 + 3.5x + x2 = 0 + -1.208333333

Combine like terms: 1.208333333 + -1.208333333 = 0.000000000
0.000000000 + 3.5x + x2 = 0 + -1.208333333
3.5x + x2 = 0 + -1.208333333

Combine like terms: 0 + -1.208333333 = -1.208333333
3.5x + x2 = -1.208333333

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = -1.208333333 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -1.208333333 + 3.0625

Combine like terms: -1.208333333 + 3.0625 = 1.854166667
3.0625 + 3.5x + x2 = 1.854166667

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 1.854166667

Calculate the square root of the right side: 1.361677887

Break this problem into two subproblems by setting 
(x + 1.75) equal to 1.361677887 and -1.361677887.


Subproblem 1
x + 1.75 = 1.361677887

Simplifying
x + 1.75 = 1.361677887

Reorder the terms:
1.75 + x = 1.361677887

Solving
1.75 + x = 1.361677887

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 1.361677887 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 1.361677887 + -1.75
x = 1.361677887 + -1.75

Combine like terms: 1.361677887 + -1.75 = -0.388322113
x = -0.388322113

Simplifying
x = -0.388322113


Subproblem 2
x + 1.75 = -1.361677887

Simplifying
x + 1.75 = -1.361677887

Reorder the terms:
1.75 + x = -1.361677887

Solving
1.75 + x = -1.361677887

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -1.361677887 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -1.361677887 + -1.75
x = -1.361677887 + -1.75

Combine like terms: -1.361677887 + -1.75 = -3.111677887
x = -3.111677887

Simplifying
x = -3.111677887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.388322113, -3.111677887}

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