x^2-5x-2.25=0

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Solution for x^2-5x-2.25=0 equation: 


Simplifying
x2 + -5x + -2.25 = 0

Reorder the terms:
-2.25 + -5x + x2 = 0

Solving
-2.25 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -5x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -5x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -5x + x2 = 0 + 2.25
-5x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-5x + x2 = 2.25

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 = 2.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 2.25 + 6.25

Combine like terms: 2.25 + 6.25 = 8.5
6.25 + -5x + x2 = 8.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.915475947 and -2.915475947.


Subproblem 1
x + -2.5 = 2.915475947

Simplifying
x + -2.5 = 2.915475947

Reorder the terms:
-2.5 + x = 2.915475947

Solving
-2.5 + x = 2.915475947

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 = 2.915475947 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.915475947 + 2.5
x = 2.915475947 + 2.5

Combine like terms: 2.915475947 + 2.5 = 5.415475947
x = 5.415475947

Simplifying
x = 5.415475947


Subproblem 2
x + -2.5 = -2.915475947

Simplifying
x + -2.5 = -2.915475947

Reorder the terms:
-2.5 + x = -2.915475947

Solving
-2.5 + x = -2.915475947

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 = -2.915475947 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.915475947 + 2.5
x = -2.915475947 + 2.5

Combine like terms: -2.915475947 + 2.5 = -0.415475947
x = -0.415475947

Simplifying
x = -0.415475947


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.415475947, -0.415475947}

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