x^2-2.75x-5=0

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


Simplifying
x2 + -2.75x + -5 = 0

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

Solving
-5 + -2.75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is -2.75x.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75x + 1.890625 + x2 = 5 + 1.890625

Reorder the terms:
1.890625 + -2.75x + x2 = 5 + 1.890625

Combine like terms: 5 + 1.890625 = 6.890625
1.890625 + -2.75x + x2 = 6.890625

Factor a perfect square on the left side:
(x + -1.375)(x + -1.375) = 6.890625

Calculate the square root of the right side: 2.625

Break this problem into two subproblems by setting 
(x + -1.375) equal to 2.625 and -2.625.


Subproblem 1
x + -1.375 = 2.625

Simplifying
x + -1.375 = 2.625

Reorder the terms:
-1.375 + x = 2.625

Solving
-1.375 + x = 2.625

Solving for variable 'x'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + x = 2.625 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + x = 2.625 + 1.375
x = 2.625 + 1.375

Combine like terms: 2.625 + 1.375 = 4
x = 4

Simplifying
x = 4


Subproblem 2
x + -1.375 = -2.625

Simplifying
x + -1.375 = -2.625

Reorder the terms:
-1.375 + x = -2.625

Solving
-1.375 + x = -2.625

Solving for variable 'x'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + x = -2.625 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + x = -2.625 + 1.375
x = -2.625 + 1.375

Combine like terms: -2.625 + 1.375 = -1.25
x = -1.25

Simplifying
x = -1.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, -1.25}

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