2k^2=21k-49

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Solution for 2k^2=21k-49 equation:


Simplifying
2k2 = 21k + -49

Reorder the terms:
2k2 = -49 + 21k

Solving
2k2 = -49 + 21k

Solving for variable 'k'.

Reorder the terms:
49 + -21k + 2k2 = -49 + 21k + 49 + -21k

Reorder the terms:
49 + -21k + 2k2 = -49 + 49 + 21k + -21k

Combine like terms: -49 + 49 = 0
49 + -21k + 2k2 = 0 + 21k + -21k
49 + -21k + 2k2 = 21k + -21k

Combine like terms: 21k + -21k = 0
49 + -21k + 2k2 = 0

Factor a trinomial.
(7 + -2k)(7 + -1k) = 0

Subproblem 1

Set the factor '(7 + -2k)' equal to zero and attempt to solve: Simplifying 7 + -2k = 0 Solving 7 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2k = 0 + -7 -2k = 0 + -7 Combine like terms: 0 + -7 = -7 -2k = -7 Divide each side by '-2'. k = 3.5 Simplifying k = 3.5

Subproblem 2

Set the factor '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7

Solution

k = {3.5, 7}

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