729=z(z-16)

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Solution for 729=z(z-16) equation:


Simplifying
729 = z(z + -16)

Reorder the terms:
729 = z(-16 + z)
729 = (-16 * z + z * z)
729 = (-16z + z2)

Solving
729 = -16z + z2

Solving for variable 'z'.

Reorder the terms:
729 + 16z + -1z2 = -16z + 16z + z2 + -1z2

Combine like terms: -16z + 16z = 0
729 + 16z + -1z2 = 0 + z2 + -1z2
729 + 16z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
729 + 16z + -1z2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-729 + -16z + z2 = 0

Move the constant term to the right:

Add '729' to each side of the equation.
-729 + -16z + 729 + z2 = 0 + 729

Reorder the terms:
-729 + 729 + -16z + z2 = 0 + 729

Combine like terms: -729 + 729 = 0
0 + -16z + z2 = 0 + 729
-16z + z2 = 0 + 729

Combine like terms: 0 + 729 = 729
-16z + z2 = 729

The z term is -16z.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16z + 64 + z2 = 729 + 64

Reorder the terms:
64 + -16z + z2 = 729 + 64

Combine like terms: 729 + 64 = 793
64 + -16z + z2 = 793

Factor a perfect square on the left side:
(z + -8)(z + -8) = 793

Calculate the square root of the right side: 28.160255681

Break this problem into two subproblems by setting 
(z + -8) equal to 28.160255681 and -28.160255681.

Subproblem 1

z + -8 = 28.160255681 Simplifying z + -8 = 28.160255681 Reorder the terms: -8 + z = 28.160255681 Solving -8 + z = 28.160255681 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z = 28.160255681 + 8 Combine like terms: -8 + 8 = 0 0 + z = 28.160255681 + 8 z = 28.160255681 + 8 Combine like terms: 28.160255681 + 8 = 36.160255681 z = 36.160255681 Simplifying z = 36.160255681

Subproblem 2

z + -8 = -28.160255681 Simplifying z + -8 = -28.160255681 Reorder the terms: -8 + z = -28.160255681 Solving -8 + z = -28.160255681 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z = -28.160255681 + 8 Combine like terms: -8 + 8 = 0 0 + z = -28.160255681 + 8 z = -28.160255681 + 8 Combine like terms: -28.160255681 + 8 = -20.160255681 z = -20.160255681 Simplifying z = -20.160255681

Solution

The solution to the problem is based on the solutions from the subproblems. z = {36.160255681, -20.160255681}

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