0.8x^2+5x+2=0

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Solution for 0.8x^2+5x+2=0 equation: 


Simplifying
0.8x2 + 5x + 2 = 0

Reorder the terms:
2 + 5x + 0.8x2 = 0

Solving
2 + 5x + 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'.
2.5 + 6.25x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 6.25x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 6.25x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 6.25x + x2 = 0 + -2.5
6.25x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
6.25x + x2 = -2.5

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = -2.5 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = -2.5 + 9.765625

Combine like terms: -2.5 + 9.765625 = 7.265625
9.765625 + 6.25x + x2 = 7.265625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 7.265625

Calculate the square root of the right side: 2.695482332

Break this problem into two subproblems by setting 
(x + 3.125) equal to 2.695482332 and -2.695482332.


Subproblem 1
x + 3.125 = 2.695482332

Simplifying
x + 3.125 = 2.695482332

Reorder the terms:
3.125 + x = 2.695482332

Solving
3.125 + x = 2.695482332

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 2.695482332 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 2.695482332 + -3.125
x = 2.695482332 + -3.125

Combine like terms: 2.695482332 + -3.125 = -0.429517668
x = -0.429517668

Simplifying
x = -0.429517668


Subproblem 2
x + 3.125 = -2.695482332

Simplifying
x + 3.125 = -2.695482332

Reorder the terms:
3.125 + x = -2.695482332

Solving
3.125 + x = -2.695482332

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -2.695482332 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -2.695482332 + -3.125
x = -2.695482332 + -3.125

Combine like terms: -2.695482332 + -3.125 = -5.820482332
x = -5.820482332

Simplifying
x = -5.820482332


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.429517668, -5.820482332}

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