k^2=7k+8

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Solution for k^2=7k+8 equation:


Simplifying
k2 = 7k + 8

Reorder the terms:
k2 = 8 + 7k

Solving
k2 = 8 + 7k

Solving for variable 'k'.

Reorder the terms:
-8 + -7k + k2 = 8 + 7k + -8 + -7k

Reorder the terms:
-8 + -7k + k2 = 8 + -8 + 7k + -7k

Combine like terms: 8 + -8 = 0
-8 + -7k + k2 = 0 + 7k + -7k
-8 + -7k + k2 = 7k + -7k

Combine like terms: 7k + -7k = 0
-8 + -7k + k2 = 0

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

Subproblem 1

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

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 = {-1, 8}

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