20x^2+110x+190=0

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Solution for 20x^2+110x+190=0 equation: 


Simplifying
20x2 + 110x + 190 = 0

Reorder the terms:
190 + 110x + 20x2 = 0

Solving
190 + 110x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(19 + 11x + 2x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(19 + 11x + 2x2)' equal to zero and attempt to solve:

Simplifying
19 + 11x + 2x2 = 0

Solving
19 + 11x + 2x2 = 0

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

Divide each side by '2'.
9.5 + 5.5x + x2 = 0

Move the constant term to the right:

Add '-9.5' to each side of the equation.
9.5 + 5.5x + -9.5 + x2 = 0 + -9.5

Reorder the terms:
9.5 + -9.5 + 5.5x + x2 = 0 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + 5.5x + x2 = 0 + -9.5
5.5x + x2 = 0 + -9.5

Combine like terms: 0 + -9.5 = -9.5
5.5x + x2 = -9.5

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = -9.5 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = -9.5 + 7.5625

Combine like terms: -9.5 + 7.5625 = -1.9375
7.5625 + 5.5x + x2 = -1.9375

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = -1.9375

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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