4k^2+16k-31=2

Solution for 4k^2+16k-31=2 equation:

Simplifying
4k2 + 16k + -31 = 2

Reorder the terms:
-31 + 16k + 4k2 = 2

Solving
-31 + 16k + 4k2 = 2

Solving for variable 'k'.

Reorder the terms:
-31 + -2 + 16k + 4k2 = 2 + -2

Combine like terms: -31 + -2 = -33
-33 + 16k + 4k2 = 2 + -2

Combine like terms: 2 + -2 = 0
-33 + 16k + 4k2 = 0

Factor a trinomial.
(-11 + -2k)(3 + -2k) = 0

Subproblem 1
Set the factor '(-11 + -2k)' equal to zero and attempt to solve:

Simplifying
-11 + -2k = 0

Solving
-11 + -2k = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2k = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2k = 0 + 11
-2k = 0 + 11

Combine like terms: 0 + 11 = 11
-2k = 11

Divide each side by '-2'.
k = -5.5

Simplifying
k = -5.5
Subproblem 2
Set the factor '(3 + -2k)' equal to zero and attempt to solve:

Simplifying
3 + -2k = 0

Solving
3 + -2k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2k = 0 + -3
-2k = 0 + -3

Combine like terms: 0 + -3 = -3
-2k = -3

Divide each side by '-2'.
k = 1.5

Simplifying
k = 1.5
Solution
k = {-5.5, 1.5}