z^2+12z=20

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Solution for z^2+12z=20 equation:


Simplifying
z2 + 12z = 20

Reorder the terms:
12z + z2 = 20

Solving
12z + z2 = 20

Solving for variable 'z'.

Reorder the terms:
-20 + 12z + z2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 12z + 20 + z2 = 0 + 20

Reorder the terms:
-20 + 20 + 12z + z2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 12z + z2 = 0 + 20
12z + z2 = 0 + 20

Combine like terms: 0 + 20 = 20
12z + z2 = 20

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 = 20 + 36

Reorder the terms:
36 + 12z + z2 = 20 + 36

Combine like terms: 20 + 36 = 56
36 + 12z + z2 = 56

Factor a perfect square on the left side:
(z + 6)(z + 6) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(z + 6) equal to 7.483314774 and -7.483314774.

Subproblem 1

z + 6 = 7.483314774 Simplifying z + 6 = 7.483314774 Reorder the terms: 6 + z = 7.483314774 Solving 6 + z = 7.483314774 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 = 7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + z = 7.483314774 + -6 z = 7.483314774 + -6 Combine like terms: 7.483314774 + -6 = 1.483314774 z = 1.483314774 Simplifying z = 1.483314774

Subproblem 2

z + 6 = -7.483314774 Simplifying z + 6 = -7.483314774 Reorder the terms: 6 + z = -7.483314774 Solving 6 + z = -7.483314774 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 = -7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + z = -7.483314774 + -6 z = -7.483314774 + -6 Combine like terms: -7.483314774 + -6 = -13.483314774 z = -13.483314774 Simplifying z = -13.483314774

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.483314774, -13.483314774}

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