1. ( k + 7 ) 2 = 289 ⇔ k + 7 = 289 or k + 7 = − 289 k = 17 − 7 = 10 or k = − 17 − 7 = − 24 2. ( 2 s − 1 ) 2 = 225 ⇔ 2 s − 1 = 225 or 2 s − 1 = − 225 2 s = 15 + 1 or 2 s = − 15 + 1 2 s = 16 or 2 s = − 14 s = 8 or s = − 7
3. ( x − 4 ) 2 = 169 ⇔ x − 4 = 169 or x − 4 = − 169 x = 13 + 4 = 17 or x = − 13 + 4 = − 9
( k + 7 ) 2 = 289 ∣ k + 7∣ = 17 k + 7 = 17 ∨ k + 7 = − 17 k = 10 ∨ k = − 24
( 2 s − 1 ) 2 = 225 ∣2 s − 1∣ = 15 2 s − 1 = 15 ∨ 2 s − 1 = − 15 2 s = 16 ∨ 2 s = − 14 s = 8 ∨ s = − 7
( x − 4 ) 2 = 169 ∣ x − 4∣ = 13 x − 4 = 13 ∨ x − 4 = − 13 x = 17 ∨ x = − 9
The solutions for the equations are as follows: For k , the solutions are 10 and − 24 ; for s , the solutions are 8 and − 7 ; and for x , the solutions are 17 and − 9 .
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