2k^2+k-8=7

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


Simplifying
2k2 + k + -8 = 7

Reorder the terms:
-8 + k + 2k2 = 7

Solving
-8 + k + 2k2 = 7

Solving for variable 'k'.

Reorder the terms:
-8 + -7 + k + 2k2 = 7 + -7

Combine like terms: -8 + -7 = -15
-15 + k + 2k2 = 7 + -7

Combine like terms: 7 + -7 = 0
-15 + k + 2k2 = 0

Factor a trinomial.
(-3 + -1k)(5 + -2k) = 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 '(5 + -2k)' equal to zero and attempt to solve: Simplifying 5 + -2k = 0 Solving 5 + -2k = 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 + -2k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2k = 0 + -5 -2k = 0 + -5 Combine like terms: 0 + -5 = -5 -2k = -5 Divide each side by '-2'. k = 2.5 Simplifying k = 2.5

Solution

k = {-3, 2.5}

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