BANK & INSURANCE (QUADRATIC EQUATION PART 1)

From I:
2x² + 12x + 10 = 0
2x² + 10x + 2x + 10 = 0
2x(x + 5) + 2(x + 5) = 0
(x + 5)(2x + 2) = 0
x = -5, -1

From II:
y² + 3y - 4 = 0
y² + 4y - y - 4 = 0
y(y + 4) - 1(y + 4) = 0
(y + 4)(y - 1) = 0
y = 1, -4

From I:
x² - 24x + 144 = 0
x² - 12x - 12x + 144 = 0
x(x - 12) - 12(x - 12) = 0
(x - 12)(x - 12) = 0
(x - 12)² = 0
x = 12, 12

From II:
y² + 15y + 56 = 0
y² + 7y + 8y + 56 = 0
y(y + 7) + 8(y + 7) = 0
(y + 7)(y + 8) = 0
y = -7, -8

From I:
3x² + 10x + 7 = 0
3x² + 3x + 7x + 7 = 0
3x(x + 1) + 7(x + 1) = 0
(x + 1)(3x + 7) = 0
x = -1, -7/3

From II:
6y² + 15y - 9 = 0
6y² + 18y - 3y - 9 = 0
6y(y + 3) - 3(y + 3) = 0
(y + 3)(6y - 3) = 0
y = -3, 1/2

From I:
3x² - 27 = 0
x² = 9
x = ±3

From II:
2y² = √(21 + 43)
2y² = 8
y² = 4
y = ±2

From I:
2x + 3y = 13
6x + 9y = 39 ----(i)

From II:
3x + 2y = 12
6x + 4y = 24 ----(ii)

Subtracting equation (ii) from equation (i), we get
5y = 15
y = 3
And, x = 2

From I:
3x² + 11x - 224 = 0
3x² - 21x + 32x - 224 = 0
3x(x - 7) + 32(x - 7) = 0
(x - 7)(3x + 32) = 0
x = 7, -32/3

From II:
y² + 13y - 48 = 0
y² + 16y - 3y - 48 = 0
y(y + 16) - 3(y + 16) = 0
(y - 3)(y + 16) = 0
y = 3, -16

From I:
x² = 9x - 20
x² - 9x + 20 = 0
x² - 5x - 4x + 20 = 0
x(x - 5) - 4(x - 5) = 0
(x - 5)(x - 4) = 0
x = 5, 4

From II:
y² - 21y = 0
y(y - 21) = 0
y = 0, 21

From I:
x² - 34x + 120 = 0
x² - 30x - 4x + 120 = 0
x(x - 30) - 4(x - 30) = 0
(x - 30)(x - 4) = 0
x = 4, 30

From II:
y² - 60x + 900 = 0
y² - 2 × 30y + 30² = 0
(y - 30)² = 0
y = 30, 30

From I:
6x² = 216
x² = 36
x = ±6

From II:
y² - 65y + 354 = 0
y² - 59y - 6y + 354 = 0
y(y - 59) - 6(y - 59) = 0
(y - 59)(y - 6) = 0
y = 6, 59

From I:
x - 256/x = 0
x² - 256 = 0
x² = 256
x = ±16

From II:
y² + 512/y = 0
y³ + 512 = 0
y³ = -512
y = -8