x^2-25x+145=0

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Solution for x^2-25x+145=0 equation: 


Simplifying
x2 + -25x + 145 = 0

Reorder the terms:
145 + -25x + x2 = 0

Solving
145 + -25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-145' to each side of the equation.
145 + -25x + -145 + x2 = 0 + -145

Reorder the terms:
145 + -145 + -25x + x2 = 0 + -145

Combine like terms: 145 + -145 = 0
0 + -25x + x2 = 0 + -145
-25x + x2 = 0 + -145

Combine like terms: 0 + -145 = -145
-25x + x2 = -145

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -145 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -145 + 156.25

Combine like terms: -145 + 156.25 = 11.25
156.25 + -25x + x2 = 11.25

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + -12.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + -12.5 = 3.354101966

Simplifying
x + -12.5 = 3.354101966

Reorder the terms:
-12.5 + x = 3.354101966

Solving
-12.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 3.354101966 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 3.354101966 + 12.5
x = 3.354101966 + 12.5

Combine like terms: 3.354101966 + 12.5 = 15.854101966
x = 15.854101966

Simplifying
x = 15.854101966


Subproblem 2
x + -12.5 = -3.354101966

Simplifying
x + -12.5 = -3.354101966

Reorder the terms:
-12.5 + x = -3.354101966

Solving
-12.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -3.354101966 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -3.354101966 + 12.5
x = -3.354101966 + 12.5

Combine like terms: -3.354101966 + 12.5 = 9.145898034
x = 9.145898034

Simplifying
x = 9.145898034


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.854101966, 9.145898034}

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