z^2-16z=-11

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Solution for z^2-16z=-11 equation:


Simplifying
z2 + -16z = -11

Reorder the terms:
-16z + z2 = -11

Solving
-16z + z2 = -11

Solving for variable 'z'.

Reorder the terms:
11 + -16z + z2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + -16z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -16z + -11 + z2 = 0 + -11

Reorder the terms:
11 + -11 + -16z + z2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -16z + z2 = 0 + -11
-16z + z2 = 0 + -11

Combine like terms: 0 + -11 = -11
-16z + z2 = -11

The z term is -16z.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16z + 64 + z2 = -11 + 64

Reorder the terms:
64 + -16z + z2 = -11 + 64

Combine like terms: -11 + 64 = 53
64 + -16z + z2 = 53

Factor a perfect square on the left side:
(z + -8)(z + -8) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(z + -8) equal to 7.280109889 and -7.280109889.

Subproblem 1

z + -8 = 7.280109889 Simplifying z + -8 = 7.280109889 Reorder the terms: -8 + z = 7.280109889 Solving -8 + z = 7.280109889 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z = 7.280109889 + 8 Combine like terms: -8 + 8 = 0 0 + z = 7.280109889 + 8 z = 7.280109889 + 8 Combine like terms: 7.280109889 + 8 = 15.280109889 z = 15.280109889 Simplifying z = 15.280109889

Subproblem 2

z + -8 = -7.280109889 Simplifying z + -8 = -7.280109889 Reorder the terms: -8 + z = -7.280109889 Solving -8 + z = -7.280109889 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z = -7.280109889 + 8 Combine like terms: -8 + 8 = 0 0 + z = -7.280109889 + 8 z = -7.280109889 + 8 Combine like terms: -7.280109889 + 8 = 0.719890111 z = 0.719890111 Simplifying z = 0.719890111

Solution

The solution to the problem is based on the solutions from the subproblems. z = {15.280109889, 0.719890111}

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