z^2-8z=-4

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Solution for z^2-8z=-4 equation:


Simplifying
z2 + -8z = -4

Reorder the terms:
-8z + z2 = -4

Solving
-8z + z2 = -4

Solving for variable 'z'.

Reorder the terms:
4 + -8z + z2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + -8z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8z + -4 + z2 = 0 + -4

Reorder the terms:
4 + -4 + -8z + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8z + z2 = 0 + -4
-8z + z2 = 0 + -4

Combine like terms: 0 + -4 = -4
-8z + z2 = -4

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 = -4 + 16

Reorder the terms:
16 + -8z + z2 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + -8z + z2 = 12

Factor a perfect square on the left side:
(z + -4)(z + -4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(z + -4) equal to 3.464101615 and -3.464101615.

Subproblem 1

z + -4 = 3.464101615 Simplifying z + -4 = 3.464101615 Reorder the terms: -4 + z = 3.464101615 Solving -4 + z = 3.464101615 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 = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + z = 3.464101615 + 4 z = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 z = 7.464101615 Simplifying z = 7.464101615

Subproblem 2

z + -4 = -3.464101615 Simplifying z + -4 = -3.464101615 Reorder the terms: -4 + z = -3.464101615 Solving -4 + z = -3.464101615 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 = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + z = -3.464101615 + 4 z = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 z = 0.535898385 Simplifying z = 0.535898385

Solution

The solution to the problem is based on the solutions from the subproblems. z = {7.464101615, 0.535898385}

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