z^2-22z=21

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Solution for z^2-22z=21 equation:


Simplifying
z2 + -22z = 21

Reorder the terms:
-22z + z2 = 21

Solving
-22z + z2 = 21

Solving for variable 'z'.

Reorder the terms:
-21 + -22z + z2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -22z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -22z + 21 + z2 = 0 + 21

Reorder the terms:
-21 + 21 + -22z + z2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -22z + z2 = 0 + 21
-22z + z2 = 0 + 21

Combine like terms: 0 + 21 = 21
-22z + z2 = 21

The z term is -22z.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22z + 121 + z2 = 21 + 121

Reorder the terms:
121 + -22z + z2 = 21 + 121

Combine like terms: 21 + 121 = 142
121 + -22z + z2 = 142

Factor a perfect square on the left side:
(z + -11)(z + -11) = 142

Calculate the square root of the right side: 11.916375288

Break this problem into two subproblems by setting 
(z + -11) equal to 11.916375288 and -11.916375288.

Subproblem 1

z + -11 = 11.916375288 Simplifying z + -11 = 11.916375288 Reorder the terms: -11 + z = 11.916375288 Solving -11 + z = 11.916375288 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + z = 11.916375288 + 11 Combine like terms: -11 + 11 = 0 0 + z = 11.916375288 + 11 z = 11.916375288 + 11 Combine like terms: 11.916375288 + 11 = 22.916375288 z = 22.916375288 Simplifying z = 22.916375288

Subproblem 2

z + -11 = -11.916375288 Simplifying z + -11 = -11.916375288 Reorder the terms: -11 + z = -11.916375288 Solving -11 + z = -11.916375288 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + z = -11.916375288 + 11 Combine like terms: -11 + 11 = 0 0 + z = -11.916375288 + 11 z = -11.916375288 + 11 Combine like terms: -11.916375288 + 11 = -0.916375288 z = -0.916375288 Simplifying z = -0.916375288

Solution

The solution to the problem is based on the solutions from the subproblems. z = {22.916375288, -0.916375288}

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