z^2+12z+18=0

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Solution for z^2+12z+18=0 equation:


Simplifying
z2 + 12z + 18 = 0

Reorder the terms:
18 + 12z + z2 = 0

Solving
18 + 12z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 12z + -18 + z2 = 0 + -18

Reorder the terms:
18 + -18 + 12z + z2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 12z + z2 = 0 + -18
12z + z2 = 0 + -18

Combine like terms: 0 + -18 = -18
12z + z2 = -18

The z term is 12z.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12z + 36 + z2 = -18 + 36

Reorder the terms:
36 + 12z + z2 = -18 + 36

Combine like terms: -18 + 36 = 18
36 + 12z + z2 = 18

Factor a perfect square on the left side:
(z + 6)(z + 6) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(z + 6) equal to 4.242640687 and -4.242640687.

Subproblem 1

z + 6 = 4.242640687 Simplifying z + 6 = 4.242640687 Reorder the terms: 6 + z = 4.242640687 Solving 6 + z = 4.242640687 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = 4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + z = 4.242640687 + -6 z = 4.242640687 + -6 Combine like terms: 4.242640687 + -6 = -1.757359313 z = -1.757359313 Simplifying z = -1.757359313

Subproblem 2

z + 6 = -4.242640687 Simplifying z + 6 = -4.242640687 Reorder the terms: 6 + z = -4.242640687 Solving 6 + z = -4.242640687 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = -4.242640687 + -6 Combine like terms: 6 + -6 = 0 0 + z = -4.242640687 + -6 z = -4.242640687 + -6 Combine like terms: -4.242640687 + -6 = -10.242640687 z = -10.242640687 Simplifying z = -10.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-1.757359313, -10.242640687}

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