z^2-4z-8=0

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Solution for z^2-4z-8=0 equation:


Simplifying
z2 + -4z + -8 = 0

Reorder the terms:
-8 + -4z + z2 = 0

Solving
-8 + -4z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -4z + 8 + z2 = 0 + 8

Reorder the terms:
-8 + 8 + -4z + z2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -4z + z2 = 0 + 8
-4z + z2 = 0 + 8

Combine like terms: 0 + 8 = 8
-4z + z2 = 8

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 = 8 + 4

Reorder the terms:
4 + -4z + z2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + -4z + z2 = 12

Factor a perfect square on the left side:
(z + -2)(z + -2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(z + -2) equal to 3.464101615 and -3.464101615.

Subproblem 1

z + -2 = 3.464101615 Simplifying z + -2 = 3.464101615 Reorder the terms: -2 + z = 3.464101615 Solving -2 + z = 3.464101615 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 = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + z = 3.464101615 + 2 z = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 z = 5.464101615 Simplifying z = 5.464101615

Subproblem 2

z + -2 = -3.464101615 Simplifying z + -2 = -3.464101615 Reorder the terms: -2 + z = -3.464101615 Solving -2 + z = -3.464101615 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 = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + z = -3.464101615 + 2 z = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 z = -1.464101615 Simplifying z = -1.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. z = {5.464101615, -1.464101615}

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