z^2-20z=27

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Solution for z^2-20z=27 equation:


Simplifying
z2 + -20z = 27

Reorder the terms:
-20z + z2 = 27

Solving
-20z + z2 = 27

Solving for variable 'z'.

Reorder the terms:
-27 + -20z + z2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -20z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -20z + 27 + z2 = 0 + 27

Reorder the terms:
-27 + 27 + -20z + z2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -20z + z2 = 0 + 27
-20z + z2 = 0 + 27

Combine like terms: 0 + 27 = 27
-20z + z2 = 27

The z term is -20z.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20z + 100 + z2 = 27 + 100

Reorder the terms:
100 + -20z + z2 = 27 + 100

Combine like terms: 27 + 100 = 127
100 + -20z + z2 = 127

Factor a perfect square on the left side:
(z + -10)(z + -10) = 127

Calculate the square root of the right side: 11.26942767

Break this problem into two subproblems by setting 
(z + -10) equal to 11.26942767 and -11.26942767.

Subproblem 1

z + -10 = 11.26942767 Simplifying z + -10 = 11.26942767 Reorder the terms: -10 + z = 11.26942767 Solving -10 + z = 11.26942767 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + z = 11.26942767 + 10 Combine like terms: -10 + 10 = 0 0 + z = 11.26942767 + 10 z = 11.26942767 + 10 Combine like terms: 11.26942767 + 10 = 21.26942767 z = 21.26942767 Simplifying z = 21.26942767

Subproblem 2

z + -10 = -11.26942767 Simplifying z + -10 = -11.26942767 Reorder the terms: -10 + z = -11.26942767 Solving -10 + z = -11.26942767 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + z = -11.26942767 + 10 Combine like terms: -10 + 10 = 0 0 + z = -11.26942767 + 10 z = -11.26942767 + 10 Combine like terms: -11.26942767 + 10 = -1.26942767 z = -1.26942767 Simplifying z = -1.26942767

Solution

The solution to the problem is based on the solutions from the subproblems. z = {21.26942767, -1.26942767}

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