z^2-16z=-13

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Solution for z^2-16z=-13 equation:


Simplifying
z2 + -16z = -13

Reorder the terms:
-16z + z2 = -13

Solving
-16z + z2 = -13

Solving for variable 'z'.

Reorder the terms:
13 + -16z + z2 = -13 + 13

Combine like terms: -13 + 13 = 0
13 + -16z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -16z + -13 + z2 = 0 + -13

Reorder the terms:
13 + -13 + -16z + z2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -16z + z2 = 0 + -13
-16z + z2 = 0 + -13

Combine like terms: 0 + -13 = -13
-16z + z2 = -13

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 = -13 + 64

Reorder the terms:
64 + -16z + z2 = -13 + 64

Combine like terms: -13 + 64 = 51
64 + -16z + z2 = 51

Factor a perfect square on the left side:
(z + -8)(z + -8) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(z + -8) equal to 7.141428429 and -7.141428429.

Subproblem 1

z + -8 = 7.141428429 Simplifying z + -8 = 7.141428429 Reorder the terms: -8 + z = 7.141428429 Solving -8 + z = 7.141428429 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 = 7.141428429 + 8 Combine like terms: -8 + 8 = 0 0 + z = 7.141428429 + 8 z = 7.141428429 + 8 Combine like terms: 7.141428429 + 8 = 15.141428429 z = 15.141428429 Simplifying z = 15.141428429

Subproblem 2

z + -8 = -7.141428429 Simplifying z + -8 = -7.141428429 Reorder the terms: -8 + z = -7.141428429 Solving -8 + z = -7.141428429 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 = -7.141428429 + 8 Combine like terms: -8 + 8 = 0 0 + z = -7.141428429 + 8 z = -7.141428429 + 8 Combine like terms: -7.141428429 + 8 = 0.858571571 z = 0.858571571 Simplifying z = 0.858571571

Solution

The solution to the problem is based on the solutions from the subproblems. z = {15.141428429, 0.858571571}

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