x^2-5x-2.75=0

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Solution for x^2-5x-2.75=0 equation: 


Simplifying
x2 + -5x + -2.75 = 0

Reorder the terms:
-2.75 + -5x + x2 = 0

Solving
-2.75 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -5x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -5x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -5x + x2 = 0 + 2.75
-5x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-5x + x2 = 2.75

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 = 2.75 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 2.75 + 6.25

Combine like terms: 2.75 + 6.25 = 9
6.25 + -5x + x2 = 9

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3 and -3.


Subproblem 1
x + -2.5 = 3

Simplifying
x + -2.5 = 3

Reorder the terms:
-2.5 + x = 3

Solving
-2.5 + x = 3

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 = 3 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3 + 2.5
x = 3 + 2.5

Combine like terms: 3 + 2.5 = 5.5
x = 5.5

Simplifying
x = 5.5


Subproblem 2
x + -2.5 = -3

Simplifying
x + -2.5 = -3

Reorder the terms:
-2.5 + x = -3

Solving
-2.5 + x = -3

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 = -3 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3 + 2.5
x = -3 + 2.5

Combine like terms: -3 + 2.5 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.5, -0.5}

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