(k+7)(k+7)=289

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Solution for (k+7)(k+7)=289 equation: 


Simplifying
(k + 7)(k + 7) = 289

Reorder the terms:
(7 + k)(k + 7) = 289

Reorder the terms:
(7 + k)(7 + k) = 289

Multiply (7 + k) * (7 + k)
(7(7 + k) + k(7 + k)) = 289
((7 * 7 + k * 7) + k(7 + k)) = 289
((49 + 7k) + k(7 + k)) = 289
(49 + 7k + (7 * k + k * k)) = 289
(49 + 7k + (7k + k2)) = 289

Combine like terms: 7k + 7k = 14k
(49 + 14k + k2) = 289

Solving
49 + 14k + k2 = 289

Solving for variable 'k'.

Reorder the terms:
49 + -289 + 14k + k2 = 289 + -289

Combine like terms: 49 + -289 = -240
-240 + 14k + k2 = 289 + -289

Combine like terms: 289 + -289 = 0
-240 + 14k + k2 = 0

Factor a trinomial.
(-24 + -1k)(10 + -1k) = 0


Subproblem 1
Set the factor '(-24 + -1k)' equal to zero and attempt to solve:

Simplifying
-24 + -1k = 0

Solving
-24 + -1k = 0

Move all terms containing k to the left, all other terms to the right.

Add '24' to each side of the equation.
-24 + 24 + -1k = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1k = 0 + 24
-1k = 0 + 24

Combine like terms: 0 + 24 = 24
-1k = 24

Divide each side by '-1'.
k = -24

Simplifying
k = -24

Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve:

Simplifying
10 + -1k = 0

Solving
10 + -1k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1k = 0 + -10
-1k = 0 + -10

Combine like terms: 0 + -10 = -10
-1k = -10

Divide each side by '-1'.
k = 10

Simplifying
k = 10
Solution
k = {-24, 10}

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