0.7x^2+3.2x+1.5=0

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Solution for 0.7x^2+3.2x+1.5=0 equation: 


Simplifying
0.7x2 + 3.2x + 1.5 = 0

Reorder the terms:
1.5 + 3.2x + 0.7x2 = 0

Solving
1.5 + 3.2x + 0.7x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.7'.
2.142857143 + 4.571428571x + x2 = 0

Move the constant term to the right:

Add '-2.142857143' to each side of the equation.
2.142857143 + 4.571428571x + -2.142857143 + x2 = 0 + -2.142857143

Reorder the terms:
2.142857143 + -2.142857143 + 4.571428571x + x2 = 0 + -2.142857143

Combine like terms: 2.142857143 + -2.142857143 = 0.000000000
0.000000000 + 4.571428571x + x2 = 0 + -2.142857143
4.571428571x + x2 = 0 + -2.142857143

Combine like terms: 0 + -2.142857143 = -2.142857143
4.571428571x + x2 = -2.142857143

The x term is 4.571428571x.  Take half its coefficient (2.285714286).
Square it (5.224489797) and add it to both sides.

Add '5.224489797' to each side of the equation.
4.571428571x + 5.224489797 + x2 = -2.142857143 + 5.224489797

Reorder the terms:
5.224489797 + 4.571428571x + x2 = -2.142857143 + 5.224489797

Combine like terms: -2.142857143 + 5.224489797 = 3.081632654
5.224489797 + 4.571428571x + x2 = 3.081632654

Factor a perfect square on the left side:
(x + 2.285714286)(x + 2.285714286) = 3.081632654

Calculate the square root of the right side: 1.755457961

Break this problem into two subproblems by setting 
(x + 2.285714286) equal to 1.755457961 and -1.755457961.


Subproblem 1
x + 2.285714286 = 1.755457961

Simplifying
x + 2.285714286 = 1.755457961

Reorder the terms:
2.285714286 + x = 1.755457961

Solving
2.285714286 + x = 1.755457961

Solving for variable 'x'.

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

Add '-2.285714286' to each side of the equation.
2.285714286 + -2.285714286 + x = 1.755457961 + -2.285714286

Combine like terms: 2.285714286 + -2.285714286 = 0.000000000
0.000000000 + x = 1.755457961 + -2.285714286
x = 1.755457961 + -2.285714286

Combine like terms: 1.755457961 + -2.285714286 = -0.530256325
x = -0.530256325

Simplifying
x = -0.530256325


Subproblem 2
x + 2.285714286 = -1.755457961

Simplifying
x + 2.285714286 = -1.755457961

Reorder the terms:
2.285714286 + x = -1.755457961

Solving
2.285714286 + x = -1.755457961

Solving for variable 'x'.

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

Add '-2.285714286' to each side of the equation.
2.285714286 + -2.285714286 + x = -1.755457961 + -2.285714286

Combine like terms: 2.285714286 + -2.285714286 = 0.000000000
0.000000000 + x = -1.755457961 + -2.285714286
x = -1.755457961 + -2.285714286

Combine like terms: -1.755457961 + -2.285714286 = -4.041172247
x = -4.041172247

Simplifying
x = -4.041172247


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.530256325, -4.041172247}

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