x^2-5.13x+6.579=0

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Solution for x^2-5.13x+6.579=0 equation: 


Simplifying
x2 + -5.13x + 6.579 = 0

Reorder the terms:
6.579 + -5.13x + x2 = 0

Solving
6.579 + -5.13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6.579' to each side of the equation.
6.579 + -5.13x + -6.579 + x2 = 0 + -6.579

Reorder the terms:
6.579 + -6.579 + -5.13x + x2 = 0 + -6.579

Combine like terms: 6.579 + -6.579 = 0.000
0.000 + -5.13x + x2 = 0 + -6.579
-5.13x + x2 = 0 + -6.579

Combine like terms: 0 + -6.579 = -6.579
-5.13x + x2 = -6.579

The x term is -5.13x.  Take half its coefficient (-2.565).
Square it (6.579225) and add it to both sides.

Add '6.579225' to each side of the equation.
-5.13x + 6.579225 + x2 = -6.579 + 6.579225

Reorder the terms:
6.579225 + -5.13x + x2 = -6.579 + 6.579225

Combine like terms: -6.579 + 6.579225 = 0.000225
6.579225 + -5.13x + x2 = 0.000225

Factor a perfect square on the left side:
(x + -2.565)(x + -2.565) = 0.000225

Calculate the square root of the right side: 0.015

Break this problem into two subproblems by setting 
(x + -2.565) equal to 0.015 and -0.015.


Subproblem 1
x + -2.565 = 0.015

Simplifying
x + -2.565 = 0.015

Reorder the terms:
-2.565 + x = 0.015

Solving
-2.565 + x = 0.015

Solving for variable 'x'.

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

Add '2.565' to each side of the equation.
-2.565 + 2.565 + x = 0.015 + 2.565

Combine like terms: -2.565 + 2.565 = 0.000
0.000 + x = 0.015 + 2.565
x = 0.015 + 2.565

Combine like terms: 0.015 + 2.565 = 2.58
x = 2.58

Simplifying
x = 2.58


Subproblem 2
x + -2.565 = -0.015

Simplifying
x + -2.565 = -0.015

Reorder the terms:
-2.565 + x = -0.015

Solving
-2.565 + x = -0.015

Solving for variable 'x'.

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

Add '2.565' to each side of the equation.
-2.565 + 2.565 + x = -0.015 + 2.565

Combine like terms: -2.565 + 2.565 = 0.000
0.000 + x = -0.015 + 2.565
x = -0.015 + 2.565

Combine like terms: -0.015 + 2.565 = 2.55
x = 2.55

Simplifying
x = 2.55


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.58, 2.55}

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