-2z^2+8z+38=0

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Solution for -2z^2+8z+38=0 equation: 


Simplifying
-2z2 + 8z + 38 = 0

Reorder the terms:
38 + 8z + -2z2 = 0

Solving
38 + 8z + -2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(19 + 4z + -1z2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(19 + 4z + -1z2)' equal to zero and attempt to solve:

Simplifying
19 + 4z + -1z2 = 0

Solving
19 + 4z + -1z2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-19 + -4z + z2 = 0

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -4z + 19 + z2 = 0 + 19

Reorder the terms:
-19 + 19 + -4z + z2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -4z + z2 = 0 + 19
-4z + z2 = 0 + 19

Combine like terms: 0 + 19 = 19
-4z + z2 = 19

The z term is -4z.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4z + 4 + z2 = 19 + 4

Reorder the terms:
4 + -4z + z2 = 19 + 4

Combine like terms: 19 + 4 = 23
4 + -4z + z2 = 23

Factor a perfect square on the left side:
(z + -2)(z + -2) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(z + -2) equal to 4.795831523 and -4.795831523.


Subproblem 1
z + -2 = 4.795831523

Simplifying
z + -2 = 4.795831523

Reorder the terms:
-2 + z = 4.795831523

Solving
-2 + z = 4.795831523

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + z = 4.795831523 + 2

Combine like terms: -2 + 2 = 0
0 + z = 4.795831523 + 2
z = 4.795831523 + 2

Combine like terms: 4.795831523 + 2 = 6.795831523
z = 6.795831523

Simplifying
z = 6.795831523


Subproblem 2
z + -2 = -4.795831523

Simplifying
z + -2 = -4.795831523

Reorder the terms:
-2 + z = -4.795831523

Solving
-2 + z = -4.795831523

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + z = -4.795831523 + 2

Combine like terms: -2 + 2 = 0
0 + z = -4.795831523 + 2
z = -4.795831523 + 2

Combine like terms: -4.795831523 + 2 = -2.795831523
z = -2.795831523

Simplifying
z = -2.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {6.795831523, -2.795831523}
Solution
z = {6.795831523, -2.795831523}

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