a) S={-1,7} b) S={-1,11}
1) Let's complete the square step by step
x²-6x = 7 Let's find the next perfect trinomial x²-6x +9 or (x-3)²
x² -6x +9 = 7 +9
(x-3)² = 16
√(x-3)² =√16
Remember square roots yield one positive and another negative number
x-3 = -4 x= -4 +3 x = -1
x-3 = 4 x= 4 +3 x = 7
2) Let's find the next perfect trinomial, dividing b =10 by 2 10 :2 = 5
x² +10x = 11
x² -5x +25 =11 +25
(x-5)² = 36
√(x-5)² = √36
Remember square roots yield one positive and another negative number
x-5 = 6 x = 6+5 x = 11
x-5 = -6 x = -6 +5 x = -1
3) Hence, the solutions are
a) S={-1,7} b) S={-1,11}