k^2-5k-16=8

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Solution for k^2-5k-16=8 equation:


Simplifying
k2 + -5k + -16 = 8

Reorder the terms:
-16 + -5k + k2 = 8

Solving
-16 + -5k + k2 = 8

Solving for variable 'k'.

Reorder the terms:
-16 + -8 + -5k + k2 = 8 + -8

Combine like terms: -16 + -8 = -24
-24 + -5k + k2 = 8 + -8

Combine like terms: 8 + -8 = 0
-24 + -5k + k2 = 0

Factor a trinomial.
(-3 + -1k)(8 + -1k) = 0

Subproblem 1

Set the factor '(-3 + -1k)' equal to zero and attempt to solve: Simplifying -3 + -1k = 0 Solving -3 + -1k = 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 + -1k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1k = 0 + 3 -1k = 0 + 3 Combine like terms: 0 + 3 = 3 -1k = 3 Divide each side by '-1'. k = -3 Simplifying k = -3

Subproblem 2

Set the factor '(8 + -1k)' equal to zero and attempt to solve: Simplifying 8 + -1k = 0 Solving 8 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1k = 0 + -8 -1k = 0 + -8 Combine like terms: 0 + -8 = -8 -1k = -8 Divide each side by '-1'. k = 8 Simplifying k = 8

Solution

k = {-3, 8}

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