z^2-11z=30

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Solution for z^2-11z=30 equation:


Simplifying
z2 + -11z = 30

Reorder the terms:
-11z + z2 = 30

Solving
-11z + z2 = 30

Solving for variable 'z'.

Reorder the terms:
-30 + -11z + z2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -11z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -11z + 30 + z2 = 0 + 30

Reorder the terms:
-30 + 30 + -11z + z2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -11z + z2 = 0 + 30
-11z + z2 = 0 + 30

Combine like terms: 0 + 30 = 30
-11z + z2 = 30

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 = 30 + 30.25

Reorder the terms:
30.25 + -11z + z2 = 30 + 30.25

Combine like terms: 30 + 30.25 = 60.25
30.25 + -11z + z2 = 60.25

Factor a perfect square on the left side:
(z + -5.5)(z + -5.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(z + -5.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

z + -5.5 = 7.762087348 Simplifying z + -5.5 = 7.762087348 Reorder the terms: -5.5 + z = 7.762087348 Solving -5.5 + z = 7.762087348 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 = 7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + z = 7.762087348 + 5.5 z = 7.762087348 + 5.5 Combine like terms: 7.762087348 + 5.5 = 13.262087348 z = 13.262087348 Simplifying z = 13.262087348

Subproblem 2

z + -5.5 = -7.762087348 Simplifying z + -5.5 = -7.762087348 Reorder the terms: -5.5 + z = -7.762087348 Solving -5.5 + z = -7.762087348 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 = -7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + z = -7.762087348 + 5.5 z = -7.762087348 + 5.5 Combine like terms: -7.762087348 + 5.5 = -2.262087348 z = -2.262087348 Simplifying z = -2.262087348

Solution

The solution to the problem is based on the solutions from the subproblems. z = {13.262087348, -2.262087348}

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