Answer:
(a) x² + 6x + 8 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
where a = 1, b = 6, and c = 8
Substituting the values, we get:
x = (-6 ± sqrt(6² - 4(1)(8))) / 2(1)
x = (-6 ± sqrt(36 - 32)) / 2
x = (-6 ± sqrt(4)) / 2
x = (-6 ± 2) / 2
x = -4 or -2
Therefore, the solutions are x = -4 or x = -2.
(b) x² + 7x + 12 = 0
We can factorize this quadratic equation as:
x² + 7x + 12 = (x + 3)(x + 4)
Therefore, the solutions are x = -3 or x = -4.
(c) y² + 7y + 10 = 0
We can factorize this quadratic equation as:
y² + 7y + 10 = (y + 2)(y + 5)
Therefore, the solutions are y = -2 or y = -5.
(d) y² + 3y - 4 = 0
We can factorize this quadratic equation as:
y² + 3y - 4 = (y + 4)(y - 1)
Therefore, the solutions are y = -4 or y = 1.
(e) x² - 2x - 8 = 0
We can factorize this quadratic equation as:
x² - 2x - 8 = (x - 4)(x + 2)
Therefore, the solutions are x = 4 or x = -2.
(f) m² - 7m + 12 = 0
We can factorize this quadratic equation as:
m² - 7m + 12 = (m - 3)(m - 4)
Therefore, the solutions are m = 3 or m = 4.
(g) y² - 10y + 25 = 0
We can factorize this quadratic equation as:
y² - 10y + 25 = (y - 5)²
Therefore, the only solution is y = 5.
(h) y² - 4y - 45 = 0
We can factorize this quadratic equation as:
y² - 4y - 45 = (y - 9)(y + 5)
Therefore, the solutions are y = 9 or y = -5.
(k) x² + 9x + 18 = 0
We can factorize this quadratic equation as:
x² +9x + 18 = (x + 3)(x + 6)
Therefore, the solutions are x = -3 or x = -6.
(m) y² - 13y + 22 = 0
We can factorize this quadratic equation as:
y² - 13y + 22 = (y - 2)(y - 11)
Therefore, the solutions are y = 2 or y = 11.
(n) x² + x - 12 = 0
We can factorize this quadratic equation as:
x² + x - 12 = (x + 4)(x - 3)
Therefore, the solutions are x = -4 or x = 3.
(p) x² - 11x + 18 = 0
We can factorize this quadratic equation as:
x² - 11x + 18 = (x - 2)(x - 9)
Therefore, the solutions are x = 2 or x = 9.
(q) y² - 14y + 48 = 0
We can factorize this quadratic equation as:
y² - 14y + 48 = (y - 6)(y - 8)
Therefore, the solutions are y = 6 or y = 8.
(s) m² - m - 56 = 0
We can factorize this quadratic equation as:
m² - m - 56 = (m- 8)(m + 7)
Therefore, the solutions are m = 8 or m = -7.
(t) y² + 22y + 96 = 0
We can factorize this quadratic equation as:
y² + 22y + 96 = (y + 12)(y + 8)
Therefore, the solutions are y = -12 or y = -8.
(v) x² - 38x + 72 = 0
We can factorize this quadratic equation as:
x² - 38x + 72 = (x - 2)(x - 36)
Therefore, the solutions are x = 2 or x = 36.
(w) x² + 14x - 51 = 0
We can factorize this quadratic equation as:
x² + 14x - 51 = (x + 17)(x - 3)
Therefore, the solutions are x = -17 or x = 3.
(y) g² - 12g - 64 = 0
We can factorize this quadratic equation as:
g² - 12g - 64 = (g - 8)(g - 4)
Therefore, the solutions are g = 8 or g = 4.
(z) y² + 22y + 121 = 0
We can factorize this quadratic equation as:
y² + 22y + 121 = (y+ 11)²
Therefore, the only solution is y = -11.
(1) y² + 10y + 24 = 0
We can factorize this quadratic equation as:
y² + 10y + 24 = (y + 4)(y + 6)
Therefore, the solutions are y = -4 or y = -6.
(1) x² - x - 56 = 0
We can factorize this quadratic equation as:
x² - x - 56 = (x - 8)(x + 7)
Therefore, the solutions are x = 8 or x = -7.
(1) x² + 23x + 22 = 0
We can factorize this quadratic equation as:
x² + 23x + 22 = (x + 1)(x + 22)
Therefore, the solutions are x = -1 or x = -22.
(0) m² - 6m - 27 = 0
We can factorize this quadratic equation as:
m² - 6m - 27 = (m - 9)(m + 3)
Therefore, the solutions are m = 9 or m = -3.
(r) x² - 15x + 56 = 0
We can factorize this quadratic equation as:
x² - 15x + 56 = (x - 7)(x - 8)
Therefore, the solutions are x = 7 or x = 8.
(u) k² - 18k - 88 = 0
We can factorize this quadratic equation as:
k² - 18k - 88 = (k - 2)(k - 16)
Therefore, the solutions are k = 2 or k = 16.
(x) y² + 32y + 240 = 0
We can factorize this quadratic equation as:
y² + 32y + 240 = (y + 12)(y + 20)
Therefore, the solutions are y = -12 or y = -20.
Hope this helps!