Let's solve each of these quadratic equations:
1) x^2 - 3x - 40 = 0
Factors of -40 that add up to -3 are -8 and 5.
(x - 8)(x + 5) = 0x = 8 or x = -5
2) x^2 + 7x + 6 = 0
Factors of 6 that add up to 7 are 1 and 6.
(x + 1)(x + 6) = 0x = -1 or x = -6
3) x^2 + 6x + 9 = 0
This quadratic equation is a perfect square trinomial.
(x + 3)(x + 3) = 0x = -3
Therefore, the solutions to the given quadratic equations are:1) x = 8 or x = -52) x = -1 or x = -63) x = -3
Let's solve each of these quadratic equations:
1) x^2 - 3x - 40 = 0
Factors of -40 that add up to -3 are -8 and 5.
(x - 8)(x + 5) = 0
x = 8 or x = -5
2) x^2 + 7x + 6 = 0
Factors of 6 that add up to 7 are 1 and 6.
(x + 1)(x + 6) = 0
x = -1 or x = -6
3) x^2 + 6x + 9 = 0
This quadratic equation is a perfect square trinomial.
(x + 3)(x + 3) = 0
x = -3
Therefore, the solutions to the given quadratic equations are:
1) x = 8 or x = -5
2) x = -1 or x = -6
3) x = -3