z^2-12z=9

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Solution for z^2-12z=9 equation:


Simplifying
z2 + -12z = 9

Reorder the terms:
-12z + z2 = 9

Solving
-12z + z2 = 9

Solving for variable 'z'.

Reorder the terms:
-9 + -12z + z2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -12z + 9 + z2 = 0 + 9

Reorder the terms:
-9 + 9 + -12z + z2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -12z + z2 = 0 + 9
-12z + z2 = 0 + 9

Combine like terms: 0 + 9 = 9
-12z + z2 = 9

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 = 9 + 36

Reorder the terms:
36 + -12z + z2 = 9 + 36

Combine like terms: 9 + 36 = 45
36 + -12z + z2 = 45

Factor a perfect square on the left side:
(z + -6)(z + -6) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(z + -6) equal to 6.708203933 and -6.708203933.

Subproblem 1

z + -6 = 6.708203933 Simplifying z + -6 = 6.708203933 Reorder the terms: -6 + z = 6.708203933 Solving -6 + z = 6.708203933 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 = 6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + z = 6.708203933 + 6 z = 6.708203933 + 6 Combine like terms: 6.708203933 + 6 = 12.708203933 z = 12.708203933 Simplifying z = 12.708203933

Subproblem 2

z + -6 = -6.708203933 Simplifying z + -6 = -6.708203933 Reorder the terms: -6 + z = -6.708203933 Solving -6 + z = -6.708203933 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 = -6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + z = -6.708203933 + 6 z = -6.708203933 + 6 Combine like terms: -6.708203933 + 6 = -0.708203933 z = -0.708203933 Simplifying z = -0.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. z = {12.708203933, -0.708203933}

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