k^2+6k-22=

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Solution for k^2+6k-22= equation:


Simplifying
k2 + 6k + -22 = 0

Reorder the terms:
-22 + 6k + k2 = 0

Solving
-22 + 6k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 6k + 22 + k2 = 0 + 22

Reorder the terms:
-22 + 22 + 6k + k2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 6k + k2 = 0 + 22
6k + k2 = 0 + 22

Combine like terms: 0 + 22 = 22
6k + k2 = 22

The k term is 6k.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6k + 9 + k2 = 22 + 9

Reorder the terms:
9 + 6k + k2 = 22 + 9

Combine like terms: 22 + 9 = 31
9 + 6k + k2 = 31

Factor a perfect square on the left side:
(k + 3)(k + 3) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(k + 3) equal to 5.567764363 and -5.567764363.

Subproblem 1

k + 3 = 5.567764363 Simplifying k + 3 = 5.567764363 Reorder the terms: 3 + k = 5.567764363 Solving 3 + k = 5.567764363 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = 5.567764363 + -3 Combine like terms: 3 + -3 = 0 0 + k = 5.567764363 + -3 k = 5.567764363 + -3 Combine like terms: 5.567764363 + -3 = 2.567764363 k = 2.567764363 Simplifying k = 2.567764363

Subproblem 2

k + 3 = -5.567764363 Simplifying k + 3 = -5.567764363 Reorder the terms: 3 + k = -5.567764363 Solving 3 + k = -5.567764363 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k = -5.567764363 + -3 Combine like terms: 3 + -3 = 0 0 + k = -5.567764363 + -3 k = -5.567764363 + -3 Combine like terms: -5.567764363 + -3 = -8.567764363 k = -8.567764363 Simplifying k = -8.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. k = {2.567764363, -8.567764363}

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