z^2-4z=76

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Solution for z^2-4z=76 equation:


Simplifying
z2 + -4z = 76

Reorder the terms:
-4z + z2 = 76

Solving
-4z + z2 = 76

Solving for variable 'z'.

Reorder the terms:
-76 + -4z + z2 = 76 + -76

Combine like terms: 76 + -76 = 0
-76 + -4z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '76' to each side of the equation.
-76 + -4z + 76 + z2 = 0 + 76

Reorder the terms:
-76 + 76 + -4z + z2 = 0 + 76

Combine like terms: -76 + 76 = 0
0 + -4z + z2 = 0 + 76
-4z + z2 = 0 + 76

Combine like terms: 0 + 76 = 76
-4z + z2 = 76

The z term is -4z.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4z + 4 + z2 = 76 + 4

Reorder the terms:
4 + -4z + z2 = 76 + 4

Combine like terms: 76 + 4 = 80
4 + -4z + z2 = 80

Factor a perfect square on the left side:
(z + -2)(z + -2) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(z + -2) equal to 8.94427191 and -8.94427191.

Subproblem 1

z + -2 = 8.94427191 Simplifying z + -2 = 8.94427191 Reorder the terms: -2 + z = 8.94427191 Solving -2 + z = 8.94427191 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 8.94427191 + 2 Combine like terms: -2 + 2 = 0 0 + z = 8.94427191 + 2 z = 8.94427191 + 2 Combine like terms: 8.94427191 + 2 = 10.94427191 z = 10.94427191 Simplifying z = 10.94427191

Subproblem 2

z + -2 = -8.94427191 Simplifying z + -2 = -8.94427191 Reorder the terms: -2 + z = -8.94427191 Solving -2 + z = -8.94427191 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = -8.94427191 + 2 Combine like terms: -2 + 2 = 0 0 + z = -8.94427191 + 2 z = -8.94427191 + 2 Combine like terms: -8.94427191 + 2 = -6.94427191 z = -6.94427191 Simplifying z = -6.94427191

Solution

The solution to the problem is based on the solutions from the subproblems. z = {10.94427191, -6.94427191}

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