30x^2+25x+20=0

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Solution for 30x^2+25x+20=0 equation: 


Simplifying
30x2 + 25x + 20 = 0

Reorder the terms:
20 + 25x + 30x2 = 0

Solving
20 + 25x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + 5x + 6x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(4 + 5x + 6x2)' equal to zero and attempt to solve:

Simplifying
4 + 5x + 6x2 = 0

Solving
4 + 5x + 6x2 = 0

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

Divide each side by '6'.
0.6666666667 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 0.8333333333x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 0.8333333333x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 0.8333333333x + x2 = 0 + -0.6666666667
0.8333333333x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
0.8333333333x + x2 = -0.6666666667

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = -0.6666666667 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = -0.6666666667 + 0.1736111111

Combine like terms: -0.6666666667 + 0.1736111111 = -0.4930555556
0.1736111111 + 0.8333333333x + x2 = -0.4930555556

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = -0.4930555556

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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