z^2-20z=-17

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Solution for z^2-20z=-17 equation:


Simplifying
z2 + -20z = -17

Reorder the terms:
-20z + z2 = -17

Solving
-20z + z2 = -17

Solving for variable 'z'.

Reorder the terms:
17 + -20z + z2 = -17 + 17

Combine like terms: -17 + 17 = 0
17 + -20z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -20z + -17 + z2 = 0 + -17

Reorder the terms:
17 + -17 + -20z + z2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -20z + z2 = 0 + -17
-20z + z2 = 0 + -17

Combine like terms: 0 + -17 = -17
-20z + z2 = -17

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 = -17 + 100

Reorder the terms:
100 + -20z + z2 = -17 + 100

Combine like terms: -17 + 100 = 83
100 + -20z + z2 = 83

Factor a perfect square on the left side:
(z + -10)(z + -10) = 83

Calculate the square root of the right side: 9.110433579

Break this problem into two subproblems by setting 
(z + -10) equal to 9.110433579 and -9.110433579.

Subproblem 1

z + -10 = 9.110433579 Simplifying z + -10 = 9.110433579 Reorder the terms: -10 + z = 9.110433579 Solving -10 + z = 9.110433579 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 = 9.110433579 + 10 Combine like terms: -10 + 10 = 0 0 + z = 9.110433579 + 10 z = 9.110433579 + 10 Combine like terms: 9.110433579 + 10 = 19.110433579 z = 19.110433579 Simplifying z = 19.110433579

Subproblem 2

z + -10 = -9.110433579 Simplifying z + -10 = -9.110433579 Reorder the terms: -10 + z = -9.110433579 Solving -10 + z = -9.110433579 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 = -9.110433579 + 10 Combine like terms: -10 + 10 = 0 0 + z = -9.110433579 + 10 z = -9.110433579 + 10 Combine like terms: -9.110433579 + 10 = 0.889566421 z = 0.889566421 Simplifying z = 0.889566421

Solution

The solution to the problem is based on the solutions from the subproblems. z = {19.110433579, 0.889566421}

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