14. Решите уравнение:

1) (2x - 3)^2 - 4(x^2 - x) = 25 4x^2 - 12x + 9 - 4x^2 + 4x = 25 -8x + 9 = 25 -8x = 16 x = -2 2) 9(2 - x^2) + (3x - 5)^2 = -2 18 - 9x^2 + 9x^2 - 30x + 25 = -2 -30x + 43 = -2 -30x = -45 x = 1.5 3) 4(x^2 - x - 1) - (2x - 1)^2 = 3 4x^2 - 4x - 4 - (4x^2 - 4x + 1) = 3 4x^2 - 4x - 4 - 4x^2 + 4x - 1 = 3 -5 = 3 (корней нет) 4) 16(2 - x - x^2) + (4x - 1)^2 = 15 32 - 16x - 16x^2 + 16x^2 - 8x + 1 = 15 -24x + 33 = 15 -24x = -18 x = 18/24 = 3/4 = 0.75 5) 5/4(10x - 3)(2x + 1) - (5x + 2)^2 = -0.25 5/4(20x^2 + 10x - 6x - 3) - (25x^2 + 20x + 4) = -0.25 5/4(20x^2 + 4x - 3) - 25x^2 - 20x - 4 = -0.25 25x^2 + 5x - 3.75 - 25x^2 - 20x - 4 = -0.25 -15x - 7.75 = -0.25 -15x = 7.5 x = -0.5 6) 3/4(6x + 5)(2x - 3) - (3x + 1)^2 = -0.25 3/4(12x^2 - 18x + 10x - 15) - (9x^2 + 6x + 1) = -0.25 3/4(12x^2 - 8x - 15) - 9x^2 - 6x - 1 = -0.25 9x^2 - 6x - 11.25 - 9x^2 - 6x - 1 = -0.25 -12x - 12.25 = -0.25 -12x = 12 x = -1 7) ((6x - 1)^2 - 1)/4 - ((5x - 2)^2 + 2x^2 + 1)/3 = 2 (36x^2 - 12x + 1 - 1)/4 - (25x^2 - 20x + 4 + 2x^2 + 1)/3 = 2 (36x^2 - 12x)/4 - (27x^2 - 20x + 5)/3 = 2 9x^2 - 3x - (9x^2 - 20/3 x + 5/3) = 2 9x^2 - 3x - 9x^2 + 20/3 x - 5/3 = 2 11/3 x = 2 + 5/3 11/3 x = 11/3 x = 1 8) ((4x - 3)^2 + 3)/2 - ((5x - 4)^2 - x^2 + 3)/3 = 1 (16x^2 - 24x + 9 + 3)/2 - (25x^2 - 40x + 16 - x^2 + 3)/3 = 1 (16x^2 - 24x + 12)/2 - (24x^2 - 40x + 19)/3 = 1 8x^2 - 12x + 6 - (8x^2 - 40/3 x + 19/3) = 1 8x^2 - 12x + 6 - 8x^2 + 40/3 x - 19/3 = 1 4/3 x = 1 - 6 + 19/3 4/3 x = -5 + 6.333 4/3 x = 4/3 x = 1