`x^2-10x=-25`
`⇔ x^2 - 10x + 25 = 0`
`⇔ x^2 - 2*5x + 5^2 = 0`
`⇔ (x-5)^2 = 0`
`⇔ x - 5 = 0`
`⇔ x = 5`
Vậy `S = {5}`
............................................
`4x^2 - 4x = -1`
`⇔ 4x^2 - 4x + 1 = 0`
`⇔ (2x)^2 - 2*2x*1 + 1^2 = 0`
`⇔ (2x-1)^2 = 0`
`⇔ 2x - 1 = 0`
`⇔ 2x = 1`
`⇔ x = 1/2`
Vậy `S = {1/2}`
.............................................
`(1-2x)^2 = (3x-2)^2`
`⇔ 1 - 4x + 4x^2 = 9x^2 - 12x + 4`
`⇔ 1 - 4x + 4x^2 - 9x^2 + 12x - 4 = 0`
`⇔ -3 + 8x - 5x^2 = 0`
`⇔ 5x^2 - 8x + 3 = 0`
`⇔ x(5x-3)-(5x-3) = 0`
`⇔ (5x-3)(x-1) = 0`
`1)` `5x - 3 = 0 ⇔ 5x = 3 ⇔ x = 3/5`
`2)` `x - 1 = 0 ⇔ x =1`
Vậy `S = {1,3/5}`
...........................................................
`x^2 - 4x = 5`
`⇔ x^2 - 4x - 5 = 0`
`⇔ x^2 + x - 5x - 5 = 0`
`⇔ x(x+1) - 5(x+1) = 0`
`⇔ (x+1)(x-5) = 0`
`1)` `x + 1 = 0 ⇔ x = -1`
`2)` `x - 5 = 0 ⇔ x = 5`
Vậy `S = {-1,5}`
.............................................................
`x-3=(3-x)^2`
`⇔ x - 3 = 9 -6x + x^2`
`⇔ x - 3 - 9 + 6x - x^2 = 0`
`⇔ 7x - 12 - x^2 = 0`
`⇔ x^2 - 7x + 12 = 0`
`⇔ x(x-3) - 4(x-3) = 0`
`⇔ (x-3)(x-4) = 0`
`1)` `x - 3 = 0 ⇔ x = 3`
`2)` `x - 4 = 0 ⇔ x = 4`
Vậy `S = {3,4}`
..........................................
`x^3 + 3/2x^2 + 3/4x + 1/8 = 1/64`
`⇔ x^3 + 3/2x^2 + 3/4x + 7/64 = 0`
`⇔ (64x^3+96x^2+48x+7)/64 = 0`
`⇔ 64x^3 + 96x^2 + 48x + 7 = 0`
`⇔ 16x^2(4x+1)+20x(4x+1)+7(4x+1) = 0`
`⇔ (4x+1)(16x^2 + 20x + 7) = 0`
`1)` `4x + 1 = 0 ⇔ 4x = -1 ⇔ x = -1/4`
`2)`
`16x^2 + 20x + 7 = 0`
`⇔ 16x^2 + 20x = -7`
`⇔ x^2 + 5/4x = -7/16`
`⇔ x^2 + 5/4x + (5/8)^2 = -7/6 + (5/8)^2`
`⇔ x^2 + 5/4x + 25/64 = -3/64`
`⇔ (x+5/8)^2 = sqrt{-3/64}`
`⇒ x ∈ ∅`
Vậy `S = {-1/4}`
