((3k+2)(3k+2))=49

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Solution for ((3k+2)(3k+2))=49 equation:


Simplifying
((3k + 2)(3k + 2)) = 49

Reorder the terms:
((2 + 3k)(3k + 2)) = 49

Reorder the terms:
((2 + 3k)(2 + 3k)) = 49

Multiply (2 + 3k) * (2 + 3k)
((2(2 + 3k) + 3k * (2 + 3k))) = 49
(((2 * 2 + 3k * 2) + 3k * (2 + 3k))) = 49
(((4 + 6k) + 3k * (2 + 3k))) = 49
((4 + 6k + (2 * 3k + 3k * 3k))) = 49
((4 + 6k + (6k + 9k2))) = 49

Combine like terms: 6k + 6k = 12k
((4 + 12k + 9k2)) = 49
(4 + 12k + 9k2) = 49

Remove parenthesis around (4 + 12k + 9k2)
4 + 12k + 9k2 = 49

Solving
4 + 12k + 9k2 = 49

Solving for variable 'k'.

Reorder the terms:
4 + -49 + 12k + 9k2 = 49 + -49

Combine like terms: 4 + -49 = -45
-45 + 12k + 9k2 = 49 + -49

Combine like terms: 49 + -49 = 0
-45 + 12k + 9k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 4k + 3k2) = 0

Factor a trinomial.
3((-3 + -1k)(5 + -3k)) = 0

Ignore the factor 3.

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 + -3k)' equal to zero and attempt to solve: Simplifying 5 + -3k = 0 Solving 5 + -3k = 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 + -3k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3k = 0 + -5 -3k = 0 + -5 Combine like terms: 0 + -5 = -5 -3k = -5 Divide each side by '-3'. k = 1.666666667 Simplifying k = 1.666666667

Solution

k = {-3, 1.666666667}

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