z^2-18z=-11

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Solution for z^2-18z=-11 equation:


Simplifying
z2 + -18z = -11

Reorder the terms:
-18z + z2 = -11

Solving
-18z + z2 = -11

Solving for variable 'z'.

Reorder the terms:
11 + -18z + z2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + -18z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -18z + -11 + z2 = 0 + -11

Reorder the terms:
11 + -11 + -18z + z2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -18z + z2 = 0 + -11
-18z + z2 = 0 + -11

Combine like terms: 0 + -11 = -11
-18z + z2 = -11

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 = -11 + 81

Reorder the terms:
81 + -18z + z2 = -11 + 81

Combine like terms: -11 + 81 = 70
81 + -18z + z2 = 70

Factor a perfect square on the left side:
(z + -9)(z + -9) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(z + -9) equal to 8.366600265 and -8.366600265.

Subproblem 1

z + -9 = 8.366600265 Simplifying z + -9 = 8.366600265 Reorder the terms: -9 + z = 8.366600265 Solving -9 + z = 8.366600265 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 = 8.366600265 + 9 Combine like terms: -9 + 9 = 0 0 + z = 8.366600265 + 9 z = 8.366600265 + 9 Combine like terms: 8.366600265 + 9 = 17.366600265 z = 17.366600265 Simplifying z = 17.366600265

Subproblem 2

z + -9 = -8.366600265 Simplifying z + -9 = -8.366600265 Reorder the terms: -9 + z = -8.366600265 Solving -9 + z = -8.366600265 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 = -8.366600265 + 9 Combine like terms: -9 + 9 = 0 0 + z = -8.366600265 + 9 z = -8.366600265 + 9 Combine like terms: -8.366600265 + 9 = 0.633399735 z = 0.633399735 Simplifying z = 0.633399735

Solution

The solution to the problem is based on the solutions from the subproblems. z = {17.366600265, 0.633399735}

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