z^2-8z-2=0

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


Simplifying
z2 + -8z + -2 = 0

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

Solving
-2 + -8z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -8z + 2 + z2 = 0 + 2

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

Combine like terms: -2 + 2 = 0
0 + -8z + z2 = 0 + 2
-8z + z2 = 0 + 2

Combine like terms: 0 + 2 = 2
-8z + z2 = 2

The z term is -8z.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8z + 16 + z2 = 2 + 16

Reorder the terms:
16 + -8z + z2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + -8z + z2 = 18

Factor a perfect square on the left side:
(z + -4)(z + -4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(z + -4) equal to 4.242640687 and -4.242640687.

Subproblem 1

z + -4 = 4.242640687 Simplifying z + -4 = 4.242640687 Reorder the terms: -4 + z = 4.242640687 Solving -4 + z = 4.242640687 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = 4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + z = 4.242640687 + 4 z = 4.242640687 + 4 Combine like terms: 4.242640687 + 4 = 8.242640687 z = 8.242640687 Simplifying z = 8.242640687

Subproblem 2

z + -4 = -4.242640687 Simplifying z + -4 = -4.242640687 Reorder the terms: -4 + z = -4.242640687 Solving -4 + z = -4.242640687 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = -4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + z = -4.242640687 + 4 z = -4.242640687 + 4 Combine like terms: -4.242640687 + 4 = -0.242640687 z = -0.242640687 Simplifying z = -0.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. z = {8.242640687, -0.242640687}

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