0.9x^2+5.4x-4=0

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Solution for 0.9x^2+5.4x-4=0 equation: 


Simplifying
0.9x2 + 5.4x + -4 = 0

Reorder the terms:
-4 + 5.4x + 0.9x2 = 0

Solving
-4 + 5.4x + 0.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.9'.
-4.444444444 + 6x + x2 = 0

Move the constant term to the right:

Add '4.444444444' to each side of the equation.
-4.444444444 + 6x + 4.444444444 + x2 = 0 + 4.444444444

Reorder the terms:
-4.444444444 + 4.444444444 + 6x + x2 = 0 + 4.444444444

Combine like terms: -4.444444444 + 4.444444444 = 0.000000000
0.000000000 + 6x + x2 = 0 + 4.444444444
6x + x2 = 0 + 4.444444444

Combine like terms: 0 + 4.444444444 = 4.444444444
6x + x2 = 4.444444444

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 4.444444444 + 9

Reorder the terms:
9 + 6x + x2 = 4.444444444 + 9

Combine like terms: 4.444444444 + 9 = 13.444444444
9 + 6x + x2 = 13.444444444

Factor a perfect square on the left side:
(x + 3)(x + 3) = 13.444444444

Calculate the square root of the right side: 3.666666667

Break this problem into two subproblems by setting 
(x + 3) equal to 3.666666667 and -3.666666667.


Subproblem 1
x + 3 = 3.666666667

Simplifying
x + 3 = 3.666666667

Reorder the terms:
3 + x = 3.666666667

Solving
3 + x = 3.666666667

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.666666667 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.666666667 + -3
x = 3.666666667 + -3

Combine like terms: 3.666666667 + -3 = 0.666666667
x = 0.666666667

Simplifying
x = 0.666666667


Subproblem 2
x + 3 = -3.666666667

Simplifying
x + 3 = -3.666666667

Reorder the terms:
3 + x = -3.666666667

Solving
3 + x = -3.666666667

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.666666667 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.666666667 + -3
x = -3.666666667 + -3

Combine like terms: -3.666666667 + -3 = -6.666666667
x = -6.666666667

Simplifying
x = -6.666666667


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.666666667, -6.666666667}

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