6x^2+44x+90=0

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Solution for 6x^2+44x+90=0 equation: 


Simplifying
6x2 + 44x + 90 = 0

Reorder the terms:
90 + 44x + 6x2 = 0

Solving
90 + 44x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + 22x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(45 + 22x + 3x2)' equal to zero and attempt to solve:

Simplifying
45 + 22x + 3x2 = 0

Solving
45 + 22x + 3x2 = 0

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

Divide each side by '3'.
15 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 7.333333333x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + 7.333333333x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 7.333333333x + x2 = 0 + -15
7.333333333x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
7.333333333x + x2 = -15

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = -15 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = -15 + 13.44444445

Combine like terms: -15 + 13.44444445 = -1.55555555
13.44444445 + 7.333333333x + x2 = -1.55555555

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = -1.55555555

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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