9k^2+k=17

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Solution for 9k^2+k=17 equation:


Simplifying
9k2 + k = 17

Reorder the terms:
k + 9k2 = 17

Solving
k + 9k2 = 17

Solving for variable 'k'.

Reorder the terms:
-17 + k + 9k2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + k + 9k2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-1.888888889 + 0.1111111111k + k2 = 0

Move the constant term to the right:

Add '1.888888889' to each side of the equation.
-1.888888889 + 0.1111111111k + 1.888888889 + k2 = 0 + 1.888888889

Reorder the terms:
-1.888888889 + 1.888888889 + 0.1111111111k + k2 = 0 + 1.888888889

Combine like terms: -1.888888889 + 1.888888889 = 0.000000000
0.000000000 + 0.1111111111k + k2 = 0 + 1.888888889
0.1111111111k + k2 = 0 + 1.888888889

Combine like terms: 0 + 1.888888889 = 1.888888889
0.1111111111k + k2 = 1.888888889

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1111111111k + 0.25 + k2 = 1.888888889 + 0.25

Reorder the terms:
0.25 + 0.1111111111k + k2 = 1.888888889 + 0.25

Combine like terms: 1.888888889 + 0.25 = 2.138888889
0.25 + 0.1111111111k + k2 = 2.138888889

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = 2.138888889

Calculate the square root of the right side: 1.462494065

Break this problem into two subproblems by setting 
(k + 0.5) equal to 1.462494065 and -1.462494065.

Subproblem 1

k + 0.5 = 1.462494065 Simplifying k + 0.5 = 1.462494065 Reorder the terms: 0.5 + k = 1.462494065 Solving 0.5 + k = 1.462494065 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = 1.462494065 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = 1.462494065 + -0.5 k = 1.462494065 + -0.5 Combine like terms: 1.462494065 + -0.5 = 0.962494065 k = 0.962494065 Simplifying k = 0.962494065

Subproblem 2

k + 0.5 = -1.462494065 Simplifying k + 0.5 = -1.462494065 Reorder the terms: 0.5 + k = -1.462494065 Solving 0.5 + k = -1.462494065 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = -1.462494065 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = -1.462494065 + -0.5 k = -1.462494065 + -0.5 Combine like terms: -1.462494065 + -0.5 = -1.962494065 k = -1.962494065 Simplifying k = -1.962494065

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.962494065, -1.962494065}

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