5x^2-2+4x=0

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Solution for 5x^2-2+4x=0 equation: 


Simplifying
5x2 + -2 + 4x = 0

Reorder the terms:
-2 + 4x + 5x2 = 0

Solving
-2 + 4x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-0.4 + 0.8x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.8x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.8x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.8x + x2 = 0 + 0.4
0.8x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.8x + x2 = 0.4

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 0.4 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 0.4 + 0.16

Combine like terms: 0.4 + 0.16 = 0.56
0.16 + 0.8x + x2 = 0.56

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.748331477 and -0.748331477.


Subproblem 1
x + 0.4 = 0.748331477

Simplifying
x + 0.4 = 0.748331477

Reorder the terms:
0.4 + x = 0.748331477

Solving
0.4 + x = 0.748331477

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 0.748331477 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 0.748331477 + -0.4
x = 0.748331477 + -0.4

Combine like terms: 0.748331477 + -0.4 = 0.348331477
x = 0.348331477

Simplifying
x = 0.348331477


Subproblem 2
x + 0.4 = -0.748331477

Simplifying
x + 0.4 = -0.748331477

Reorder the terms:
0.4 + x = -0.748331477

Solving
0.4 + x = -0.748331477

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -0.748331477 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -0.748331477 + -0.4
x = -0.748331477 + -0.4

Combine like terms: -0.748331477 + -0.4 = -1.148331477
x = -1.148331477

Simplifying
x = -1.148331477


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.348331477, -1.148331477}

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