Given 4x² = (3y-5z:4) ², find

x if y=x-2 and z=2y

x = 2/5 or x = - 2/3

Step-by-step explanation:

y = x - 2

z = 2y = 2 (x - 2) = 2x - 4

4x² = (3y - 5z : 4) ²

Substitute y with x - 2. Substitute z with 2x - 4.

4x² = [3 (x - 2) - 5 (2x - 4) : 4]²

16 * 4x² = [3 (x - 2) * 4 - 5 (2x - 4) : 4 * 4]²

64x² = [12 (x - 2) - 5 (2x - 4) ]²

64x² = (12x - 24 - 10x + 20) ²

64x² = (2x - 4) ²

64x² = 4x² - 16x + 16

60x² + 16x - 16 = 0

15x² + 4x - 4 = 0

ac = 15 * (-4) = - 60

-6 * 10 = - 60

-6 + 10 = 4

15x² - 6x + 10x - 4 = 0

(15x² - 6x) + (10x - 4) = 0

3x (5x - 2) + 2 (5x - 2) = 0

(5x - 2) (3x + 2) = 0

5x - 2 = 0 or 3x + 2 = 0

5x = 2 or 3x = - 2

x = 2/5 or x = - 2/3