z^2-12z=32

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Solution for z^2-12z=32 equation:


Simplifying
z2 + -12z = 32

Reorder the terms:
-12z + z2 = 32

Solving
-12z + z2 = 32

Solving for variable 'z'.

Reorder the terms:
-32 + -12z + z2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + -12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -12z + 32 + z2 = 0 + 32

Reorder the terms:
-32 + 32 + -12z + z2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -12z + z2 = 0 + 32
-12z + z2 = 0 + 32

Combine like terms: 0 + 32 = 32
-12z + z2 = 32

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 = 32 + 36

Reorder the terms:
36 + -12z + z2 = 32 + 36

Combine like terms: 32 + 36 = 68
36 + -12z + z2 = 68

Factor a perfect square on the left side:
(z + -6)(z + -6) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(z + -6) equal to 8.246211251 and -8.246211251.

Subproblem 1

z + -6 = 8.246211251 Simplifying z + -6 = 8.246211251 Reorder the terms: -6 + z = 8.246211251 Solving -6 + z = 8.246211251 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 = 8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + z = 8.246211251 + 6 z = 8.246211251 + 6 Combine like terms: 8.246211251 + 6 = 14.246211251 z = 14.246211251 Simplifying z = 14.246211251

Subproblem 2

z + -6 = -8.246211251 Simplifying z + -6 = -8.246211251 Reorder the terms: -6 + z = -8.246211251 Solving -6 + z = -8.246211251 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 = -8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + z = -8.246211251 + 6 z = -8.246211251 + 6 Combine like terms: -8.246211251 + 6 = -2.246211251 z = -2.246211251 Simplifying z = -2.246211251

Solution

The solution to the problem is based on the solutions from the subproblems. z = {14.246211251, -2.246211251}

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