Completing the Square: Questions 📝

Solve the following quadratic equations by completing the square. Leave your answers in simplified exact form (i.e., as fractions or surds where necessary).

Question 1

Solve: $x^2 + 6x - 7 = 0$

Question 2

Solve: $x^2 - 8x + 10 = 0$

Question 3

Solve: $x^2 + 5x - 3 = 0$

Question 4

Solve: $x^2 - 12x + 36 = 0$

Question 5

Solve: $2x^2 + 12x - 4 = 0$

Question 6

Solve: $3x^2 - 6x - 5 = 0$

Question 7

Solve: $x^2 - 3x - 1 = 0$

Question 8

Solve: $5x^2 + 10x + 1 = 0$

Question 9

Solve: $x^2 + 2x + 5 = 0$

Question 10

Solve: $2x^2 - 5x - 4 = 0$