z^2-8z=47

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Solution for z^2-8z=47 equation:


Simplifying
z2 + -8z = 47

Reorder the terms:
-8z + z2 = 47

Solving
-8z + z2 = 47

Solving for variable 'z'.

Reorder the terms:
-47 + -8z + z2 = 47 + -47

Combine like terms: 47 + -47 = 0
-47 + -8z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -8z + 47 + z2 = 0 + 47

Reorder the terms:
-47 + 47 + -8z + z2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -8z + z2 = 0 + 47
-8z + z2 = 0 + 47

Combine like terms: 0 + 47 = 47
-8z + z2 = 47

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 = 47 + 16

Reorder the terms:
16 + -8z + z2 = 47 + 16

Combine like terms: 47 + 16 = 63
16 + -8z + z2 = 63

Factor a perfect square on the left side:
(z + -4)(z + -4) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(z + -4) equal to 7.937253933 and -7.937253933.

Subproblem 1

z + -4 = 7.937253933 Simplifying z + -4 = 7.937253933 Reorder the terms: -4 + z = 7.937253933 Solving -4 + z = 7.937253933 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 = 7.937253933 + 4 Combine like terms: -4 + 4 = 0 0 + z = 7.937253933 + 4 z = 7.937253933 + 4 Combine like terms: 7.937253933 + 4 = 11.937253933 z = 11.937253933 Simplifying z = 11.937253933

Subproblem 2

z + -4 = -7.937253933 Simplifying z + -4 = -7.937253933 Reorder the terms: -4 + z = -7.937253933 Solving -4 + z = -7.937253933 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 = -7.937253933 + 4 Combine like terms: -4 + 4 = 0 0 + z = -7.937253933 + 4 z = -7.937253933 + 4 Combine like terms: -7.937253933 + 4 = -3.937253933 z = -3.937253933 Simplifying z = -3.937253933

Solution

The solution to the problem is based on the solutions from the subproblems. z = {11.937253933, -3.937253933}

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