k^2=3k+10

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Solution for k^2=3k+10 equation:


Simplifying
k2 = 3k + 10

Reorder the terms:
k2 = 10 + 3k

Solving
k2 = 10 + 3k

Solving for variable 'k'.

Reorder the terms:
-10 + -3k + k2 = 10 + 3k + -10 + -3k

Reorder the terms:
-10 + -3k + k2 = 10 + -10 + 3k + -3k

Combine like terms: 10 + -10 = 0
-10 + -3k + k2 = 0 + 3k + -3k
-10 + -3k + k2 = 3k + -3k

Combine like terms: 3k + -3k = 0
-10 + -3k + k2 = 0

Factor a trinomial.
(-2 + -1k)(5 + -1k) = 0

Subproblem 1

Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 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 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2

Subproblem 2

Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5

Solution

k = {-2, 5}

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