z^2-11z+14=0

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Solution for z^2-11z+14=0 equation:


Simplifying
z2 + -11z + 14 = 0

Reorder the terms:
14 + -11z + z2 = 0

Solving
14 + -11z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -11z + -14 + z2 = 0 + -14

Reorder the terms:
14 + -14 + -11z + z2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -11z + z2 = 0 + -14
-11z + z2 = 0 + -14

Combine like terms: 0 + -14 = -14
-11z + z2 = -14

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 = -14 + 30.25

Reorder the terms:
30.25 + -11z + z2 = -14 + 30.25

Combine like terms: -14 + 30.25 = 16.25
30.25 + -11z + z2 = 16.25

Factor a perfect square on the left side:
(z + -5.5)(z + -5.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(z + -5.5) equal to 4.031128874 and -4.031128874.

Subproblem 1

z + -5.5 = 4.031128874 Simplifying z + -5.5 = 4.031128874 Reorder the terms: -5.5 + z = 4.031128874 Solving -5.5 + z = 4.031128874 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 = 4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + z = 4.031128874 + 5.5 z = 4.031128874 + 5.5 Combine like terms: 4.031128874 + 5.5 = 9.531128874 z = 9.531128874 Simplifying z = 9.531128874

Subproblem 2

z + -5.5 = -4.031128874 Simplifying z + -5.5 = -4.031128874 Reorder the terms: -5.5 + z = -4.031128874 Solving -5.5 + z = -4.031128874 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 = -4.031128874 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + z = -4.031128874 + 5.5 z = -4.031128874 + 5.5 Combine like terms: -4.031128874 + 5.5 = 1.468871126 z = 1.468871126 Simplifying z = 1.468871126

Solution

The solution to the problem is based on the solutions from the subproblems. z = {9.531128874, 1.468871126}

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