z^2-10z=-11

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Solution for z^2-10z=-11 equation:


Simplifying
z2 + -10z = -11

Reorder the terms:
-10z + z2 = -11

Solving
-10z + z2 = -11

Solving for variable 'z'.

Reorder the terms:
11 + -10z + z2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + -10z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -10z + -11 + z2 = 0 + -11

Reorder the terms:
11 + -11 + -10z + z2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -10z + z2 = 0 + -11
-10z + z2 = 0 + -11

Combine like terms: 0 + -11 = -11
-10z + z2 = -11

The z term is -10z.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10z + 25 + z2 = -11 + 25

Reorder the terms:
25 + -10z + z2 = -11 + 25

Combine like terms: -11 + 25 = 14
25 + -10z + z2 = 14

Factor a perfect square on the left side:
(z + -5)(z + -5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(z + -5) equal to 3.741657387 and -3.741657387.

Subproblem 1

z + -5 = 3.741657387 Simplifying z + -5 = 3.741657387 Reorder the terms: -5 + z = 3.741657387 Solving -5 + z = 3.741657387 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = 3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + z = 3.741657387 + 5 z = 3.741657387 + 5 Combine like terms: 3.741657387 + 5 = 8.741657387 z = 8.741657387 Simplifying z = 8.741657387

Subproblem 2

z + -5 = -3.741657387 Simplifying z + -5 = -3.741657387 Reorder the terms: -5 + z = -3.741657387 Solving -5 + z = -3.741657387 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = -3.741657387 + 5 Combine like terms: -5 + 5 = 0 0 + z = -3.741657387 + 5 z = -3.741657387 + 5 Combine like terms: -3.741657387 + 5 = 1.258342613 z = 1.258342613 Simplifying z = 1.258342613

Solution

The solution to the problem is based on the solutions from the subproblems. z = {8.741657387, 1.258342613}

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