x^2-4x-29=0

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


Simplifying
x2 + -4x + -29 = 0

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

Solving
-29 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

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

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

Combine like terms: 29 + 4 = 33
4 + -4x + x2 = 33

Factor a perfect square on the left side:
(x + -2)(x + -2) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -2) equal to 5.744562647 and -5.744562647.


Subproblem 1
x + -2 = 5.744562647

Simplifying
x + -2 = 5.744562647

Reorder the terms:
-2 + x = 5.744562647

Solving
-2 + x = 5.744562647

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 5.744562647 + 2

Combine like terms: -2 + 2 = 0
0 + x = 5.744562647 + 2
x = 5.744562647 + 2

Combine like terms: 5.744562647 + 2 = 7.744562647
x = 7.744562647

Simplifying
x = 7.744562647


Subproblem 2
x + -2 = -5.744562647

Simplifying
x + -2 = -5.744562647

Reorder the terms:
-2 + x = -5.744562647

Solving
-2 + x = -5.744562647

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -5.744562647 + 2

Combine like terms: -2 + 2 = 0
0 + x = -5.744562647 + 2
x = -5.744562647 + 2

Combine like terms: -5.744562647 + 2 = -3.744562647
x = -3.744562647

Simplifying
x = -3.744562647


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.744562647, -3.744562647}

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