z^2-8z=64

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Solution for z^2-8z=64 equation:


Simplifying
z2 + -8z = 64

Reorder the terms:
-8z + z2 = 64

Solving
-8z + z2 = 64

Solving for variable 'z'.

Reorder the terms:
-64 + -8z + z2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + -8z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -8z + 64 + z2 = 0 + 64

Reorder the terms:
-64 + 64 + -8z + z2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -8z + z2 = 0 + 64
-8z + z2 = 0 + 64

Combine like terms: 0 + 64 = 64
-8z + z2 = 64

The z term is -8z.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8z + 16 + z2 = 64 + 16

Reorder the terms:
16 + -8z + z2 = 64 + 16

Combine like terms: 64 + 16 = 80
16 + -8z + z2 = 80

Factor a perfect square on the left side:
(z + -4)(z + -4) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(z + -4) equal to 8.94427191 and -8.94427191.

Subproblem 1

z + -4 = 8.94427191 Simplifying z + -4 = 8.94427191 Reorder the terms: -4 + z = 8.94427191 Solving -4 + z = 8.94427191 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = 8.94427191 + 4 Combine like terms: -4 + 4 = 0 0 + z = 8.94427191 + 4 z = 8.94427191 + 4 Combine like terms: 8.94427191 + 4 = 12.94427191 z = 12.94427191 Simplifying z = 12.94427191

Subproblem 2

z + -4 = -8.94427191 Simplifying z + -4 = -8.94427191 Reorder the terms: -4 + z = -8.94427191 Solving -4 + z = -8.94427191 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + z = -8.94427191 + 4 Combine like terms: -4 + 4 = 0 0 + z = -8.94427191 + 4 z = -8.94427191 + 4 Combine like terms: -8.94427191 + 4 = -4.94427191 z = -4.94427191 Simplifying z = -4.94427191

Solution

The solution to the problem is based on the solutions from the subproblems. z = {12.94427191, -4.94427191}

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