2x^2-3x-8.22=0

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Solution for 2x^2-3x-8.22=0 equation: 


Simplifying
2x2 + -3x + -8.22 = 0

Reorder the terms:
-8.22 + -3x + 2x2 = 0

Solving
-8.22 + -3x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-4.11 + -1.5x + x2 = 0

Move the constant term to the right:

Add '4.11' to each side of the equation.
-4.11 + -1.5x + 4.11 + x2 = 0 + 4.11

Reorder the terms:
-4.11 + 4.11 + -1.5x + x2 = 0 + 4.11

Combine like terms: -4.11 + 4.11 = 0.00
0.00 + -1.5x + x2 = 0 + 4.11
-1.5x + x2 = 0 + 4.11

Combine like terms: 0 + 4.11 = 4.11
-1.5x + x2 = 4.11

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 4.11 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 4.11 + 0.5625

Combine like terms: 4.11 + 0.5625 = 4.6725
0.5625 + -1.5x + x2 = 4.6725

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 4.6725

Calculate the square root of the right side: 2.161596632

Break this problem into two subproblems by setting 
(x + -0.75) equal to 2.161596632 and -2.161596632.


Subproblem 1
x + -0.75 = 2.161596632

Simplifying
x + -0.75 = 2.161596632

Reorder the terms:
-0.75 + x = 2.161596632

Solving
-0.75 + x = 2.161596632

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 2.161596632 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 2.161596632 + 0.75
x = 2.161596632 + 0.75

Combine like terms: 2.161596632 + 0.75 = 2.911596632
x = 2.911596632

Simplifying
x = 2.911596632


Subproblem 2
x + -0.75 = -2.161596632

Simplifying
x + -0.75 = -2.161596632

Reorder the terms:
-0.75 + x = -2.161596632

Solving
-0.75 + x = -2.161596632

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -2.161596632 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -2.161596632 + 0.75
x = -2.161596632 + 0.75

Combine like terms: -2.161596632 + 0.75 = -1.411596632
x = -1.411596632

Simplifying
x = -1.411596632


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.911596632, -1.411596632}

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