z^2+11z=18

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


Simplifying
z2 + 11z = 18

Reorder the terms:
11z + z2 = 18

Solving
11z + z2 = 18

Solving for variable 'z'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The z term is 11z.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11z + 30.25 + z2 = 18 + 30.25

Reorder the terms:
30.25 + 11z + z2 = 18 + 30.25

Combine like terms: 18 + 30.25 = 48.25
30.25 + 11z + z2 = 48.25

Factor a perfect square on the left side:
(z + 5.5)(z + 5.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(z + 5.5) equal to 6.946221995 and -6.946221995.

Subproblem 1

z + 5.5 = 6.946221995 Simplifying z + 5.5 = 6.946221995 Reorder the terms: 5.5 + z = 6.946221995 Solving 5.5 + z = 6.946221995 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + z = 6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + z = 6.946221995 + -5.5 z = 6.946221995 + -5.5 Combine like terms: 6.946221995 + -5.5 = 1.446221995 z = 1.446221995 Simplifying z = 1.446221995

Subproblem 2

z + 5.5 = -6.946221995 Simplifying z + 5.5 = -6.946221995 Reorder the terms: 5.5 + z = -6.946221995 Solving 5.5 + z = -6.946221995 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + z = -6.946221995 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + z = -6.946221995 + -5.5 z = -6.946221995 + -5.5 Combine like terms: -6.946221995 + -5.5 = -12.446221995 z = -12.446221995 Simplifying z = -12.446221995

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.446221995, -12.446221995}

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