1. complete the square to form a perfect square trinomial. 8x + x² + __
a. 16
b. 4
c. 8
d. 2

2. solve the equation by completing the square. x² + 4x = 12
a. 3, -4
b. -6, 2
c. 4, -4
d. -4, 3

3. find the number of real solutions using the discriminant. x² + 9x + 4 = 0
a. 0
b. 1
c. 2

4. find the number of real solutions using the discriminant. x² - 6x - 7 = 0
a. 2
b. 1
c. 0

1. x² + 8x + 16
    x² + 4x + 4x + 16
    x(x) + x(4) + 4(x) + 4(4)
    x(x + 4) + 4(x + 4)
    (x + 4)(x + 4)
    (x + 4)²
The answer is A.

2.                           x² + 4x = 12
                        x² + 4x + 4 = 12 + 4
                        x² + 4x + 4 = 16
                x² + 2x + 2x + 4 = 16
    x(x) + x(2) + 2(x) + 2(2) = 16
             x(x + 2) + 2(x + 2) = 16
                     (x + 2)(x + 2) = 16
                              (x + 2)² = 16
                            √(x + 2)² = √16
                                 x + 2 = ±4
                                    - 2    - 2
                                      x = -2 ± 4
                                      x = -2 + 4    or    x = -2 - 4
                                      x = 2       or        x = -6
The answer is B.

3. x² + 9x + 4 = 0
    Δ = b² - 4ac
    Δ = (9)² - 4(1)(4)
    Δ = 81 - 4(4)
    Δ = 81 - 16
    Δ = 65
THe answer is C.

4. x² - 6x - 7 = 0
    Δ = b² - 4ac
    Δ = (-6)² - 4(1)(-7)
    Δ = 36 - 4(-7)
    Δ = 36 + 28
    Δ = 64
The answer is A.

They sought new allies to germany tried to get mexico to join and put pressure on the us. the us joined the allies because of the lucitania