x^2-6.75x+4.5=0

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Solution for x^2-6.75x+4.5=0 equation: 


Simplifying
x2 + -6.75x + 4.5 = 0

Reorder the terms:
4.5 + -6.75x + x2 = 0

Solving
4.5 + -6.75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -6.75x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -6.75x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -6.75x + x2 = 0 + -4.5
-6.75x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-6.75x + x2 = -4.5

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = -4.5 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = -4.5 + 11.390625

Combine like terms: -4.5 + 11.390625 = 6.890625
11.390625 + -6.75x + x2 = 6.890625

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 6.890625

Calculate the square root of the right side: 2.625

Break this problem into two subproblems by setting 
(x + -3.375) equal to 2.625 and -2.625.


Subproblem 1
x + -3.375 = 2.625

Simplifying
x + -3.375 = 2.625

Reorder the terms:
-3.375 + x = 2.625

Solving
-3.375 + x = 2.625

Solving for variable 'x'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + x = 2.625 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + x = 2.625 + 3.375
x = 2.625 + 3.375

Combine like terms: 2.625 + 3.375 = 6
x = 6

Simplifying
x = 6


Subproblem 2
x + -3.375 = -2.625

Simplifying
x + -3.375 = -2.625

Reorder the terms:
-3.375 + x = -2.625

Solving
-3.375 + x = -2.625

Solving for variable 'x'.

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

Add '3.375' to each side of the equation.
-3.375 + 3.375 + x = -2.625 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + x = -2.625 + 3.375
x = -2.625 + 3.375

Combine like terms: -2.625 + 3.375 = 0.75
x = 0.75

Simplifying
x = 0.75


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6, 0.75}

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