x^2-29x+99=0

Solution for x^2-29x+99=0 equation:

Simplifying
x2 + -29x + 99 = 0

Reorder the terms:
99 + -29x + x2 = 0

Solving
99 + -29x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-99' to each side of the equation.
99 + -29x + -99 + x2 = 0 + -99

Reorder the terms:
99 + -99 + -29x + x2 = 0 + -99

Combine like terms: 99 + -99 = 0
0 + -29x + x2 = 0 + -99
-29x + x2 = 0 + -99

Combine like terms: 0 + -99 = -99
-29x + x2 = -99

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 = -99 + 210.25

Reorder the terms:
210.25 + -29x + x2 = -99 + 210.25

Combine like terms: -99 + 210.25 = 111.25
210.25 + -29x + x2 = 111.25

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 111.25

Calculate the square root of the right side: 10.547511555

Break this problem into two subproblems by setting 
(x + -14.5) equal to 10.547511555 and -10.547511555.

Subproblem 1
x + -14.5 = 10.547511555

Simplifying
x + -14.5 = 10.547511555

Reorder the terms:
-14.5 + x = 10.547511555

Solving
-14.5 + x = 10.547511555

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 = 10.547511555 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = 10.547511555 + 14.5
x = 10.547511555 + 14.5

Combine like terms: 10.547511555 + 14.5 = 25.047511555
x = 25.047511555

Simplifying
x = 25.047511555

Subproblem 2
x + -14.5 = -10.547511555

Simplifying
x + -14.5 = -10.547511555

Reorder the terms:
-14.5 + x = -10.547511555

Solving
-14.5 + x = -10.547511555

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 = -10.547511555 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = -10.547511555 + 14.5
x = -10.547511555 + 14.5

Combine like terms: -10.547511555 + 14.5 = 3.952488445
x = 3.952488445

Simplifying
x = 3.952488445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.047511555, 3.952488445}