z^2-18z=-15

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Solution for z^2-18z=-15 equation:


Simplifying
z2 + -18z = -15

Reorder the terms:
-18z + z2 = -15

Solving
-18z + z2 = -15

Solving for variable 'z'.

Reorder the terms:
15 + -18z + z2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -18z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -18z + -15 + z2 = 0 + -15

Reorder the terms:
15 + -15 + -18z + z2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -18z + z2 = 0 + -15
-18z + z2 = 0 + -15

Combine like terms: 0 + -15 = -15
-18z + z2 = -15

The z term is -18z.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18z + 81 + z2 = -15 + 81

Reorder the terms:
81 + -18z + z2 = -15 + 81

Combine like terms: -15 + 81 = 66
81 + -18z + z2 = 66

Factor a perfect square on the left side:
(z + -9)(z + -9) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(z + -9) equal to 8.124038405 and -8.124038405.

Subproblem 1

z + -9 = 8.124038405 Simplifying z + -9 = 8.124038405 Reorder the terms: -9 + z = 8.124038405 Solving -9 + z = 8.124038405 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = 8.124038405 + 9 Combine like terms: -9 + 9 = 0 0 + z = 8.124038405 + 9 z = 8.124038405 + 9 Combine like terms: 8.124038405 + 9 = 17.124038405 z = 17.124038405 Simplifying z = 17.124038405

Subproblem 2

z + -9 = -8.124038405 Simplifying z + -9 = -8.124038405 Reorder the terms: -9 + z = -8.124038405 Solving -9 + z = -8.124038405 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = -8.124038405 + 9 Combine like terms: -9 + 9 = 0 0 + z = -8.124038405 + 9 z = -8.124038405 + 9 Combine like terms: -8.124038405 + 9 = 0.875961595 z = 0.875961595 Simplifying z = 0.875961595

Solution

The solution to the problem is based on the solutions from the subproblems. z = {17.124038405, 0.875961595}

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