x^2-29x+189=0

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Solution for x^2-29x+189=0 equation: 


Simplifying
x2 + -29x + 189 = 0

Reorder the terms:
189 + -29x + x2 = 0

Solving
189 + -29x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-189' to each side of the equation.
189 + -29x + -189 + x2 = 0 + -189

Reorder the terms:
189 + -189 + -29x + x2 = 0 + -189

Combine like terms: 189 + -189 = 0
0 + -29x + x2 = 0 + -189
-29x + x2 = 0 + -189

Combine like terms: 0 + -189 = -189
-29x + x2 = -189

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 = -189 + 210.25

Reorder the terms:
210.25 + -29x + x2 = -189 + 210.25

Combine like terms: -189 + 210.25 = 21.25
210.25 + -29x + x2 = 21.25

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + -14.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
x + -14.5 = 4.609772229

Simplifying
x + -14.5 = 4.609772229

Reorder the terms:
-14.5 + x = 4.609772229

Solving
-14.5 + x = 4.609772229

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 = 4.609772229 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = 4.609772229 + 14.5
x = 4.609772229 + 14.5

Combine like terms: 4.609772229 + 14.5 = 19.109772229
x = 19.109772229

Simplifying
x = 19.109772229


Subproblem 2
x + -14.5 = -4.609772229

Simplifying
x + -14.5 = -4.609772229

Reorder the terms:
-14.5 + x = -4.609772229

Solving
-14.5 + x = -4.609772229

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 = -4.609772229 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + x = -4.609772229 + 14.5
x = -4.609772229 + 14.5

Combine like terms: -4.609772229 + 14.5 = 9.890227771
x = 9.890227771

Simplifying
x = 9.890227771


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.109772229, 9.890227771}

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