k^2-18k+23=0

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Solution for k^2-18k+23=0 equation:


Simplifying
k2 + -18k + 23 = 0

Reorder the terms:
23 + -18k + k2 = 0

Solving
23 + -18k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + -18k + -23 + k2 = 0 + -23

Reorder the terms:
23 + -23 + -18k + k2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -18k + k2 = 0 + -23
-18k + k2 = 0 + -23

Combine like terms: 0 + -23 = -23
-18k + k2 = -23

The k term is -18k.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18k + 81 + k2 = -23 + 81

Reorder the terms:
81 + -18k + k2 = -23 + 81

Combine like terms: -23 + 81 = 58
81 + -18k + k2 = 58

Factor a perfect square on the left side:
(k + -9)(k + -9) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(k + -9) equal to 7.615773106 and -7.615773106.

Subproblem 1

k + -9 = 7.615773106 Simplifying k + -9 = 7.615773106 Reorder the terms: -9 + k = 7.615773106 Solving -9 + k = 7.615773106 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + k = 7.615773106 + 9 Combine like terms: -9 + 9 = 0 0 + k = 7.615773106 + 9 k = 7.615773106 + 9 Combine like terms: 7.615773106 + 9 = 16.615773106 k = 16.615773106 Simplifying k = 16.615773106

Subproblem 2

k + -9 = -7.615773106 Simplifying k + -9 = -7.615773106 Reorder the terms: -9 + k = -7.615773106 Solving -9 + k = -7.615773106 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + k = -7.615773106 + 9 Combine like terms: -9 + 9 = 0 0 + k = -7.615773106 + 9 k = -7.615773106 + 9 Combine like terms: -7.615773106 + 9 = 1.384226894 k = 1.384226894 Simplifying k = 1.384226894

Solution

The solution to the problem is based on the solutions from the subproblems. k = {16.615773106, 1.384226894}

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