Answer:
  x² + 2x + 1 = 0
∴ x² + x + x + 1 = 0
∴ x (x + 1) + 1(x + 1) = 0
∴ (x + 1) (x + 1) = 0
∴ x + 1 = 0 OR x + 1 = 0
∴ x = − 1 OR x = − 1
∴ − 1 is the solution of the given equation.

Answer:
  x² − 2x + 1 = 0
∴ x² − x − x + 1 = 0
∴ x (x − 1) − 1(x − 1) = 0
∴ (x − 1) (x − 1) = 0
∴ x − 1 = 0 OR x − 1 = 0
∴ x = 1 OR x = 1
∴ 1 is the solution of the given equation.

Answer:
  x² + 4x + 4 = 0
∴ x² + 2x + 2x + 4 = 0
∴ x (x + 2) + 2(x + 2) = 0
∴ (x + 2) (x + 2) = 0
∴ x + 2 = 0 OR x + 2 = 0
∴ x = − 2 OR x = − 2
∴ − 2 is the solution of the given equation.

Answer:
  x² − 4x + 4 = 0
∴ x² − 2x − 2x + 4 = 0
∴ x (x − 2) − 2(x − 2) = 0
∴ (x − 2) (x − 2) = 0
∴ x − 2 = 0 OR x − 2 = 0
∴ x = 2 OR x = 2
∴ 2 is the solution of the given equation.

Answer:
  x² − 484 = 0
∴ x² − 22² = 0
∴ (x + 22) (x − 22) = 0 [∵ a² − b² = (a + b)(a − b)]
∴ x + 22 = 0 OR x − 22 = 0
∴ x = − 22 OR x = 22
∴ 22, − 22 are the solutions of the given equation.

Answer:
  x² − 5x + 6 = 0
∴ x² − 3x − 2x + 6 = 0
∴ x (x − 3) − 2(x − 3) = 0
∴ (x − 3) (x − 2) = 0
∴ x − 3 = 0 OR x − 2 = 0
∴ x = 3 OR x = 2
∴ 3, 2 are the solutions of the given equation.

Answer:
  y² + 10y + 24 = 0
∴ y² + 6y + 4y + 24 = 0
∴ y (y + 6) + 4(y + 6) = 0
∴ (y + 6) (y + 4) = 0
∴ y + 6 = 0 OR y + 4 = 0
∴ y = − 6 OR y = − 4
∴ − 6, − 4 are the solutions of the given equation.

Answer:
 m² − 13m − 30 = 0
∴ m² − 15m + 2m − 30 = 0
∴ m (m − 15) + 2(m − 15) = 0
∴ (m − 15) (m + 2) = 0
∴ m − 15 = 0 OR m + 2 = 0
∴ m = 15 OR m = − 2
∴ 15, − 2 are the solutions of the given equation.
Or you can also write it as:  Solution Set = {15, − 2}

Answer:
 m² − 17m + 60 = 0
∴ m² − 12m − 5m + 60 = 0
∴ m (m − 12) + 5(m − 12) = 0
∴ (m − 12) (m − 5) = 0
∴ m − 12 = 0 OR m − 5 = 0
∴ m = 12 OR m = 5
∴ 12, 5 are the solutions of the given equation.
Or you can also write it as:  Solution Set = {12, 5}

Answer:
  m² − 19 = 0
∴ m² − ($\sqrt{19}$)² = 0
∴ (x + $\sqrt{19}$) (x − $\sqrt{19}$) = 0 [∵ a² − b² = (a + b)(a − b)]
∴ x + $\sqrt{19}$ = 0 OR x − $\sqrt{19}$ = 0
∴ x = − $\sqrt{19}$ OR x = $\sqrt{19}$
∴ $\sqrt{19}$, − $\sqrt{19}$ are the solutions of the given equation.