k^2+14k+17=-7

Solution for k^2+14k+17=-7 equation:

Simplifying
k2 + 14k + 17 = -7

Reorder the terms:
17 + 14k + k2 = -7

Solving
17 + 14k + k2 = -7

Solving for variable 'k'.

Reorder the terms:
17 + 7 + 14k + k2 = -7 + 7

Combine like terms: 17 + 7 = 24
24 + 14k + k2 = -7 + 7

Combine like terms: -7 + 7 = 0
24 + 14k + k2 = 0

Factor a trinomial.
(12 + k)(2 + k) = 0

Subproblem 1
Set the factor '(12 + k)' equal to zero and attempt to solve:

Simplifying
12 + k = 0

Solving
12 + k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + k = 0 + -12

Combine like terms: 12 + -12 = 0
0 + k = 0 + -12
k = 0 + -12

Combine like terms: 0 + -12 = -12
k = -12

Simplifying
k = -12
Subproblem 2
Set the factor '(2 + k)' equal to zero and attempt to solve:

Simplifying
2 + k = 0

Solving
2 + k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + k = 0 + -2
k = 0 + -2

Combine like terms: 0 + -2 = -2
k = -2

Simplifying
k = -2
Solution
k = {-12, -2}