x^2-29x-4=0

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Solution for x^2-29x-4=0 equation: 


Simplifying
x2 + -29x + -4 = 0

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

Solving
-4 + -29x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -29x + 4 + x2 = 0 + 4

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

Combine like terms: -4 + 4 = 0
0 + -29x + x2 = 0 + 4
-29x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-29x + x2 = 4

The x term is -29x.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29x + 210.25 + x2 = 4 + 210.25

Reorder the terms:
210.25 + -29x + x2 = 4 + 210.25

Combine like terms: 4 + 210.25 = 214.25
210.25 + -29x + x2 = 214.25

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 214.25

Calculate the square root of the right side: 14.637281168

Break this problem into two subproblems by setting 
(x + -14.5) equal to 14.637281168 and -14.637281168.


Subproblem 1
x + -14.5 = 14.637281168

Simplifying
x + -14.5 = 14.637281168

Reorder the terms:
-14.5 + x = 14.637281168

Solving
-14.5 + x = 14.637281168

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = 14.637281168 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = 14.637281168 + 14.5
x = 14.637281168 + 14.5

Combine like terms: 14.637281168 + 14.5 = 29.137281168
x = 29.137281168

Simplifying
x = 29.137281168


Subproblem 2
x + -14.5 = -14.637281168

Simplifying
x + -14.5 = -14.637281168

Reorder the terms:
-14.5 + x = -14.637281168

Solving
-14.5 + x = -14.637281168

Solving for variable 'x'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + x = -14.637281168 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = -14.637281168 + 14.5
x = -14.637281168 + 14.5

Combine like terms: -14.637281168 + 14.5 = -0.137281168
x = -0.137281168

Simplifying
x = -0.137281168


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.137281168, -0.137281168}

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