3.2x^2+4.4x+1.5=0

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Solution for 3.2x^2+4.4x+1.5=0 equation: 


Simplifying
3.2x2 + 4.4x + 1.5 = 0

Reorder the terms:
1.5 + 4.4x + 3.2x2 = 0

Solving
1.5 + 4.4x + 3.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.2'.
0.46875 + 1.375x + x2 = 0

Move the constant term to the right:

Add '-0.46875' to each side of the equation.
0.46875 + 1.375x + -0.46875 + x2 = 0 + -0.46875

Reorder the terms:
0.46875 + -0.46875 + 1.375x + x2 = 0 + -0.46875

Combine like terms: 0.46875 + -0.46875 = 0.00000
0.00000 + 1.375x + x2 = 0 + -0.46875
1.375x + x2 = 0 + -0.46875

Combine like terms: 0 + -0.46875 = -0.46875
1.375x + x2 = -0.46875

The x term is 1.375x.  Take half its coefficient (0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
1.375x + 0.47265625 + x2 = -0.46875 + 0.47265625

Reorder the terms:
0.47265625 + 1.375x + x2 = -0.46875 + 0.47265625

Combine like terms: -0.46875 + 0.47265625 = 0.00390625
0.47265625 + 1.375x + x2 = 0.00390625

Factor a perfect square on the left side:
(x + 0.6875)(x + 0.6875) = 0.00390625

Calculate the square root of the right side: 0.0625

Break this problem into two subproblems by setting 
(x + 0.6875) equal to 0.0625 and -0.0625.


Subproblem 1
x + 0.6875 = 0.0625

Simplifying
x + 0.6875 = 0.0625

Reorder the terms:
0.6875 + x = 0.0625

Solving
0.6875 + x = 0.0625

Solving for variable 'x'.

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

Add '-0.6875' to each side of the equation.
0.6875 + -0.6875 + x = 0.0625 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + x = 0.0625 + -0.6875
x = 0.0625 + -0.6875

Combine like terms: 0.0625 + -0.6875 = -0.625
x = -0.625

Simplifying
x = -0.625


Subproblem 2
x + 0.6875 = -0.0625

Simplifying
x + 0.6875 = -0.0625

Reorder the terms:
0.6875 + x = -0.0625

Solving
0.6875 + x = -0.0625

Solving for variable 'x'.

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

Add '-0.6875' to each side of the equation.
0.6875 + -0.6875 + x = -0.0625 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + x = -0.0625 + -0.6875
x = -0.0625 + -0.6875

Combine like terms: -0.0625 + -0.6875 = -0.75
x = -0.75

Simplifying
x = -0.75


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.625, -0.75}

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