z^2-14z=-44

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Solution for z^2-14z=-44 equation:


Simplifying
z2 + -14z = -44

Reorder the terms:
-14z + z2 = -44

Solving
-14z + z2 = -44

Solving for variable 'z'.

Reorder the terms:
44 + -14z + z2 = -44 + 44

Combine like terms: -44 + 44 = 0
44 + -14z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + -14z + -44 + z2 = 0 + -44

Reorder the terms:
44 + -44 + -14z + z2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + -14z + z2 = 0 + -44
-14z + z2 = 0 + -44

Combine like terms: 0 + -44 = -44
-14z + z2 = -44

The z term is -14z.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14z + 49 + z2 = -44 + 49

Reorder the terms:
49 + -14z + z2 = -44 + 49

Combine like terms: -44 + 49 = 5
49 + -14z + z2 = 5

Factor a perfect square on the left side:
(z + -7)(z + -7) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(z + -7) equal to 2.236067978 and -2.236067978.

Subproblem 1

z + -7 = 2.236067978 Simplifying z + -7 = 2.236067978 Reorder the terms: -7 + z = 2.236067978 Solving -7 + z = 2.236067978 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = 2.236067978 + 7 Combine like terms: -7 + 7 = 0 0 + z = 2.236067978 + 7 z = 2.236067978 + 7 Combine like terms: 2.236067978 + 7 = 9.236067978 z = 9.236067978 Simplifying z = 9.236067978

Subproblem 2

z + -7 = -2.236067978 Simplifying z + -7 = -2.236067978 Reorder the terms: -7 + z = -2.236067978 Solving -7 + z = -2.236067978 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = -2.236067978 + 7 Combine like terms: -7 + 7 = 0 0 + z = -2.236067978 + 7 z = -2.236067978 + 7 Combine like terms: -2.236067978 + 7 = 4.763932022 z = 4.763932022 Simplifying z = 4.763932022

Solution

The solution to the problem is based on the solutions from the subproblems. z = {9.236067978, 4.763932022}

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