-8z^2-3z-16=0

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Solution for -8z^2-3z-16=0 equation: 


Simplifying
-8z2 + -3z + -16 = 0

Reorder the terms:
-16 + -3z + -8z2 = 0

Solving
-16 + -3z + -8z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 3z + 8z2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(16 + 3z + 8z2)' equal to zero and attempt to solve:

Simplifying
16 + 3z + 8z2 = 0

Solving
16 + 3z + 8z2 = 0

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

Divide each side by '8'.
2 + 0.375z + z2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.375z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + 0.375z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.375z + z2 = 0 + -2
0.375z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.375z + z2 = -2

The z term is 0.375z.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375z + 0.03515625 + z2 = -2 + 0.03515625

Reorder the terms:
0.03515625 + 0.375z + z2 = -2 + 0.03515625

Combine like terms: -2 + 0.03515625 = -1.96484375
0.03515625 + 0.375z + z2 = -1.96484375

Factor a perfect square on the left side:
(z + 0.1875)(z + 0.1875) = -1.96484375

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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