z^2-8z-12=0

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Solution for z^2-8z-12=0 equation:


Simplifying
z2 + -8z + -12 = 0

Reorder the terms:
-12 + -8z + z2 = 0

Solving
-12 + -8z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -8z + 12 + z2 = 0 + 12

Reorder the terms:
-12 + 12 + -8z + z2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -8z + z2 = 0 + 12
-8z + z2 = 0 + 12

Combine like terms: 0 + 12 = 12
-8z + z2 = 12

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 = 12 + 16

Reorder the terms:
16 + -8z + z2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + -8z + z2 = 28

Factor a perfect square on the left side:
(z + -4)(z + -4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(z + -4) equal to 5.291502622 and -5.291502622.

Subproblem 1

z + -4 = 5.291502622 Simplifying z + -4 = 5.291502622 Reorder the terms: -4 + z = 5.291502622 Solving -4 + z = 5.291502622 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 = 5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + z = 5.291502622 + 4 z = 5.291502622 + 4 Combine like terms: 5.291502622 + 4 = 9.291502622 z = 9.291502622 Simplifying z = 9.291502622

Subproblem 2

z + -4 = -5.291502622 Simplifying z + -4 = -5.291502622 Reorder the terms: -4 + z = -5.291502622 Solving -4 + z = -5.291502622 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 = -5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + z = -5.291502622 + 4 z = -5.291502622 + 4 Combine like terms: -5.291502622 + 4 = -1.291502622 z = -1.291502622 Simplifying z = -1.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. z = {9.291502622, -1.291502622}

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