z^2+12z=146

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Solution for z^2+12z=146 equation:


Simplifying
z2 + 12z = 146

Reorder the terms:
12z + z2 = 146

Solving
12z + z2 = 146

Solving for variable 'z'.

Reorder the terms:
-146 + 12z + z2 = 146 + -146

Combine like terms: 146 + -146 = 0
-146 + 12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '146' to each side of the equation.
-146 + 12z + 146 + z2 = 0 + 146

Reorder the terms:
-146 + 146 + 12z + z2 = 0 + 146

Combine like terms: -146 + 146 = 0
0 + 12z + z2 = 0 + 146
12z + z2 = 0 + 146

Combine like terms: 0 + 146 = 146
12z + z2 = 146

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 = 146 + 36

Reorder the terms:
36 + 12z + z2 = 146 + 36

Combine like terms: 146 + 36 = 182
36 + 12z + z2 = 182

Factor a perfect square on the left side:
(z + 6)(z + 6) = 182

Calculate the square root of the right side: 13.490737563

Break this problem into two subproblems by setting 
(z + 6) equal to 13.490737563 and -13.490737563.

Subproblem 1

z + 6 = 13.490737563 Simplifying z + 6 = 13.490737563 Reorder the terms: 6 + z = 13.490737563 Solving 6 + z = 13.490737563 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 = 13.490737563 + -6 Combine like terms: 6 + -6 = 0 0 + z = 13.490737563 + -6 z = 13.490737563 + -6 Combine like terms: 13.490737563 + -6 = 7.490737563 z = 7.490737563 Simplifying z = 7.490737563

Subproblem 2

z + 6 = -13.490737563 Simplifying z + 6 = -13.490737563 Reorder the terms: 6 + z = -13.490737563 Solving 6 + z = -13.490737563 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 = -13.490737563 + -6 Combine like terms: 6 + -6 = 0 0 + z = -13.490737563 + -6 z = -13.490737563 + -6 Combine like terms: -13.490737563 + -6 = -19.490737563 z = -19.490737563 Simplifying z = -19.490737563

Solution

The solution to the problem is based on the solutions from the subproblems. z = {7.490737563, -19.490737563}

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