x^2-5x+6.25=5

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Solution for x^2-5x+6.25=5 equation: 


Simplifying
x2 + -5x + 6.25 = 5

Reorder the terms:
6.25 + -5x + x2 = 5

Solving
6.25 + -5x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
6.25 + -5 + -5x + x2 = 5 + -5

Combine like terms: 6.25 + -5 = 1.25
1.25 + -5x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
1.25 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -5x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -5x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -5x + x2 = 0 + -1.25
-5x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-5x + x2 = -1.25

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -1.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -1.25 + 6.25

Combine like terms: -1.25 + 6.25 = 5
6.25 + -5x + x2 = 5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -2.5 = 2.236067978

Simplifying
x + -2.5 = 2.236067978

Reorder the terms:
-2.5 + x = 2.236067978

Solving
-2.5 + x = 2.236067978

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.236067978 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.236067978 + 2.5
x = 2.236067978 + 2.5

Combine like terms: 2.236067978 + 2.5 = 4.736067978
x = 4.736067978

Simplifying
x = 4.736067978


Subproblem 2
x + -2.5 = -2.236067978

Simplifying
x + -2.5 = -2.236067978

Reorder the terms:
-2.5 + x = -2.236067978

Solving
-2.5 + x = -2.236067978

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.236067978 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.236067978 + 2.5
x = -2.236067978 + 2.5

Combine like terms: -2.236067978 + 2.5 = 0.263932022
x = 0.263932022

Simplifying
x = 0.263932022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.736067978, 0.263932022}

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