z^2-10z+17=0

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Solution for z^2-10z+17=0 equation:


Simplifying
z2 + -10z + 17 = 0

Reorder the terms:
17 + -10z + z2 = 0

Solving
17 + -10z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -10z + -17 + z2 = 0 + -17

Reorder the terms:
17 + -17 + -10z + z2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -10z + z2 = 0 + -17
-10z + z2 = 0 + -17

Combine like terms: 0 + -17 = -17
-10z + z2 = -17

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 = -17 + 25

Reorder the terms:
25 + -10z + z2 = -17 + 25

Combine like terms: -17 + 25 = 8
25 + -10z + z2 = 8

Factor a perfect square on the left side:
(z + -5)(z + -5) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(z + -5) equal to 2.828427125 and -2.828427125.

Subproblem 1

z + -5 = 2.828427125 Simplifying z + -5 = 2.828427125 Reorder the terms: -5 + z = 2.828427125 Solving -5 + z = 2.828427125 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 = 2.828427125 + 5 Combine like terms: -5 + 5 = 0 0 + z = 2.828427125 + 5 z = 2.828427125 + 5 Combine like terms: 2.828427125 + 5 = 7.828427125 z = 7.828427125 Simplifying z = 7.828427125

Subproblem 2

z + -5 = -2.828427125 Simplifying z + -5 = -2.828427125 Reorder the terms: -5 + z = -2.828427125 Solving -5 + z = -2.828427125 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 = -2.828427125 + 5 Combine like terms: -5 + 5 = 0 0 + z = -2.828427125 + 5 z = -2.828427125 + 5 Combine like terms: -2.828427125 + 5 = 2.171572875 z = 2.171572875 Simplifying z = 2.171572875

Solution

The solution to the problem is based on the solutions from the subproblems. z = {7.828427125, 2.171572875}

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