16x^2+24x+6=-30

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Solution for 16x^2+24x+6=-30 equation: 


Simplifying
16x2 + 24x + 6 = -30

Reorder the terms:
6 + 24x + 16x2 = -30

Solving
6 + 24x + 16x2 = -30

Solving for variable 'x'.

Reorder the terms:
6 + 30 + 24x + 16x2 = -30 + 30

Combine like terms: 6 + 30 = 36
36 + 24x + 16x2 = -30 + 30

Combine like terms: -30 + 30 = 0
36 + 24x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + 6x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(9 + 6x + 4x2)' equal to zero and attempt to solve:

Simplifying
9 + 6x + 4x2 = 0

Solving
9 + 6x + 4x2 = 0

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

Divide each side by '4'.
2.25 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + 1.5x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 1.5x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 1.5x + x2 = 0 + -2.25
1.5x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
1.5x + x2 = -2.25

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -2.25 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -2.25 + 0.5625

Combine like terms: -2.25 + 0.5625 = -1.6875
0.5625 + 1.5x + x2 = -1.6875

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -1.6875

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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