x^2-5x+5.76=0

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Solution for x^2-5x+5.76=0 equation: 


Simplifying
x2 + -5x + 5.76 = 0

Reorder the terms:
5.76 + -5x + x2 = 0

Solving
5.76 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5.76' to each side of the equation.
5.76 + -5x + -5.76 + x2 = 0 + -5.76

Reorder the terms:
5.76 + -5.76 + -5x + x2 = 0 + -5.76

Combine like terms: 5.76 + -5.76 = 0.00
0.00 + -5x + x2 = 0 + -5.76
-5x + x2 = 0 + -5.76

Combine like terms: 0 + -5.76 = -5.76
-5x + x2 = -5.76

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 = -5.76 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -5.76 + 6.25

Combine like terms: -5.76 + 6.25 = 0.49
6.25 + -5x + x2 = 0.49

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 0.49

Calculate the square root of the right side: 0.7

Break this problem into two subproblems by setting 
(x + -2.5) equal to 0.7 and -0.7.


Subproblem 1
x + -2.5 = 0.7

Simplifying
x + -2.5 = 0.7

Reorder the terms:
-2.5 + x = 0.7

Solving
-2.5 + x = 0.7

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 = 0.7 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 0.7 + 2.5
x = 0.7 + 2.5

Combine like terms: 0.7 + 2.5 = 3.2
x = 3.2

Simplifying
x = 3.2


Subproblem 2
x + -2.5 = -0.7

Simplifying
x + -2.5 = -0.7

Reorder the terms:
-2.5 + x = -0.7

Solving
-2.5 + x = -0.7

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 = -0.7 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -0.7 + 2.5
x = -0.7 + 2.5

Combine like terms: -0.7 + 2.5 = 1.8
x = 1.8

Simplifying
x = 1.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.2, 1.8}

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