40x^2+6x+30=0

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Solution for 40x^2+6x+30=0 equation: 


Simplifying
40x2 + 6x + 30 = 0

Reorder the terms:
30 + 6x + 40x2 = 0

Solving
30 + 6x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 3x + 20x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + 3x + 20x2)' equal to zero and attempt to solve:

Simplifying
15 + 3x + 20x2 = 0

Solving
15 + 3x + 20x2 = 0

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

Divide each side by '20'.
0.75 + 0.15x + x2 = 0.0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 0.15x + -0.75 + x2 = 0.0 + -0.75

Reorder the terms:
0.75 + -0.75 + 0.15x + x2 = 0.0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 0.15x + x2 = 0.0 + -0.75
0.15x + x2 = 0.0 + -0.75

Combine like terms: 0.0 + -0.75 = -0.75
0.15x + x2 = -0.75

The x term is 0.15x.  Take half its coefficient (0.075).
Square it (0.005625) and add it to both sides.

Add '0.005625' to each side of the equation.
0.15x + 0.005625 + x2 = -0.75 + 0.005625

Reorder the terms:
0.005625 + 0.15x + x2 = -0.75 + 0.005625

Combine like terms: -0.75 + 0.005625 = -0.744375
0.005625 + 0.15x + x2 = -0.744375

Factor a perfect square on the left side:
(x + 0.075)(x + 0.075) = -0.744375

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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