40x^2+2x+24=0

Solution for 40x^2+2x+24=0 equation:

Simplifying
40x2 + 2x + 24 = 0

Reorder the terms:
24 + 2x + 40x2 = 0

Solving
24 + 2x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + x + 20x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + x + 20x2)' equal to zero and attempt to solve:

Simplifying
12 + x + 20x2 = 0

Solving
12 + x + 20x2 = 0

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

Divide each side by '20'.
0.6 + 0.05x + x2 = 0.0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 0.05x + -0.6 + x2 = 0.0 + -0.6

Reorder the terms:
0.6 + -0.6 + 0.05x + x2 = 0.0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 0.05x + x2 = 0.0 + -0.6
0.05x + x2 = 0.0 + -0.6

Combine like terms: 0.0 + -0.6 = -0.6
0.05x + x2 = -0.6

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.05x + 0.25 + x2 = -0.6 + 0.25

Reorder the terms:
0.25 + 0.05x + x2 = -0.6 + 0.25

Combine like terms: -0.6 + 0.25 = -0.35
0.25 + 0.05x + x2 = -0.35

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.35

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.