z^2-8z=-9

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Solution for z^2-8z=-9 equation:


Simplifying
z2 + -8z = -9

Reorder the terms:
-8z + z2 = -9

Solving
-8z + z2 = -9

Solving for variable 'z'.

Reorder the terms:
9 + -8z + z2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -8z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -8z + -9 + z2 = 0 + -9

Reorder the terms:
9 + -9 + -8z + z2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8z + z2 = 0 + -9
-8z + z2 = 0 + -9

Combine like terms: 0 + -9 = -9
-8z + z2 = -9

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 = -9 + 16

Reorder the terms:
16 + -8z + z2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + -8z + z2 = 7

Factor a perfect square on the left side:
(z + -4)(z + -4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(z + -4) equal to 2.645751311 and -2.645751311.

Subproblem 1

z + -4 = 2.645751311 Simplifying z + -4 = 2.645751311 Reorder the terms: -4 + z = 2.645751311 Solving -4 + z = 2.645751311 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 = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + z = 2.645751311 + 4 z = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 z = 6.645751311 Simplifying z = 6.645751311

Subproblem 2

z + -4 = -2.645751311 Simplifying z + -4 = -2.645751311 Reorder the terms: -4 + z = -2.645751311 Solving -4 + z = -2.645751311 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 = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + z = -2.645751311 + 4 z = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 z = 1.354248689 Simplifying z = 1.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. z = {6.645751311, 1.354248689}

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