x^2+29x-100=0

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Solution for x^2+29x-100=0 equation: 


Simplifying
x2 + 29x + -100 = 0

Reorder the terms:
-100 + 29x + x2 = 0

Solving
-100 + 29x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 29x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 29x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 29x + x2 = 0 + 100
29x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
29x + x2 = 100

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 = 100 + 210.25

Reorder the terms:
210.25 + 29x + x2 = 100 + 210.25

Combine like terms: 100 + 210.25 = 310.25
210.25 + 29x + x2 = 310.25

Factor a perfect square on the left side:
(x + 14.5)(x + 14.5) = 310.25

Calculate the square root of the right side: 17.613914954

Break this problem into two subproblems by setting 
(x + 14.5) equal to 17.613914954 and -17.613914954.


Subproblem 1
x + 14.5 = 17.613914954

Simplifying
x + 14.5 = 17.613914954

Reorder the terms:
14.5 + x = 17.613914954

Solving
14.5 + x = 17.613914954

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 = 17.613914954 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + x = 17.613914954 + -14.5
x = 17.613914954 + -14.5

Combine like terms: 17.613914954 + -14.5 = 3.113914954
x = 3.113914954

Simplifying
x = 3.113914954


Subproblem 2
x + 14.5 = -17.613914954

Simplifying
x + 14.5 = -17.613914954

Reorder the terms:
14.5 + x = -17.613914954

Solving
14.5 + x = -17.613914954

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 = -17.613914954 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + x = -17.613914954 + -14.5
x = -17.613914954 + -14.5

Combine like terms: -17.613914954 + -14.5 = -32.113914954
x = -32.113914954

Simplifying
x = -32.113914954


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.113914954, -32.113914954}

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