z^2-14z=-11

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


Simplifying
z2 + -14z = -11

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

Solving
-14z + z2 = -11

Solving for variable 'z'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -11 + 49

Reorder the terms:
49 + -14z + z2 = -11 + 49

Combine like terms: -11 + 49 = 38
49 + -14z + z2 = 38

Factor a perfect square on the left side:
(z + -7)(z + -7) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(z + -7) equal to 6.164414003 and -6.164414003.

Subproblem 1

z + -7 = 6.164414003 Simplifying z + -7 = 6.164414003 Reorder the terms: -7 + z = 6.164414003 Solving -7 + z = 6.164414003 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 = 6.164414003 + 7 Combine like terms: -7 + 7 = 0 0 + z = 6.164414003 + 7 z = 6.164414003 + 7 Combine like terms: 6.164414003 + 7 = 13.164414003 z = 13.164414003 Simplifying z = 13.164414003

Subproblem 2

z + -7 = -6.164414003 Simplifying z + -7 = -6.164414003 Reorder the terms: -7 + z = -6.164414003 Solving -7 + z = -6.164414003 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 = -6.164414003 + 7 Combine like terms: -7 + 7 = 0 0 + z = -6.164414003 + 7 z = -6.164414003 + 7 Combine like terms: -6.164414003 + 7 = 0.835585997 z = 0.835585997 Simplifying z = 0.835585997

Solution

The solution to the problem is based on the solutions from the subproblems. z = {13.164414003, 0.835585997}

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