0.8x^2+3x+2.1=0

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Solution for 0.8x^2+3x+2.1=0 equation: 


Simplifying
0.8x2 + 3x + 2.1 = 0

Reorder the terms:
2.1 + 3x + 0.8x2 = 0

Solving
2.1 + 3x + 0.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.8'.
2.625 + 3.75x + x2 = 0

Move the constant term to the right:

Add '-2.625' to each side of the equation.
2.625 + 3.75x + -2.625 + x2 = 0 + -2.625

Reorder the terms:
2.625 + -2.625 + 3.75x + x2 = 0 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + 3.75x + x2 = 0 + -2.625
3.75x + x2 = 0 + -2.625

Combine like terms: 0 + -2.625 = -2.625
3.75x + x2 = -2.625

The x term is 3.75x.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75x + 3.515625 + x2 = -2.625 + 3.515625

Reorder the terms:
3.515625 + 3.75x + x2 = -2.625 + 3.515625

Combine like terms: -2.625 + 3.515625 = 0.890625
3.515625 + 3.75x + x2 = 0.890625

Factor a perfect square on the left side:
(x + 1.875)(x + 1.875) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + 1.875) equal to 0.943729304 and -0.943729304.


Subproblem 1
x + 1.875 = 0.943729304

Simplifying
x + 1.875 = 0.943729304

Reorder the terms:
1.875 + x = 0.943729304

Solving
1.875 + x = 0.943729304

Solving for variable 'x'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + x = 0.943729304 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + x = 0.943729304 + -1.875
x = 0.943729304 + -1.875

Combine like terms: 0.943729304 + -1.875 = -0.931270696
x = -0.931270696

Simplifying
x = -0.931270696


Subproblem 2
x + 1.875 = -0.943729304

Simplifying
x + 1.875 = -0.943729304

Reorder the terms:
1.875 + x = -0.943729304

Solving
1.875 + x = -0.943729304

Solving for variable 'x'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + x = -0.943729304 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + x = -0.943729304 + -1.875
x = -0.943729304 + -1.875

Combine like terms: -0.943729304 + -1.875 = -2.818729304
x = -2.818729304

Simplifying
x = -2.818729304


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.931270696, -2.818729304}

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