$(x + 4)^2 = 3x + 40$
$x^2 + 8x + 16 - 3x - 40 = 0$
$x^2 + 5x - 24 = 0$
$D = 5^2 - 4 * 1 * (-24) = 25 + 96 = 121$
$x = \frac{-5 ± \sqrt{121}}{2}$
$x_1 = \frac{-5 - 11}{2} = \frac{-16}{2} = -8$
$x_2 = \frac{-5 + 11}{2} = \frac{6}{2} = 3$
Ответ:
$x_1 = -8$;
$x_2 = 3$.

$(2x - 3)^2 = 11x - 19$
$4x^2 - 12x + 9 - 11x + 19 = 0$
$4x^2 - 23x + 28 = 0$
$D = 23^2 - 4 * 4 * 28 = 529 - 448 = 81$
$x = \frac{23 ± \sqrt{81}}{8}$
$x_1 = \frac{23 - 9}{8} = \frac{14}{8} = \frac{7}{4} = 1\frac{3}{4}$
$x_2 = \frac{23 + 9}{8} = \frac{32}{8} = 4$
Ответ:
$x_1 = 1\frac{3}{4}$;
$x_2 = 4$.

$3(x + 4)^2 = 10x + 32$
$3(x^2 + 8x + 16) - 10x + 32 = 0$
$3x^2 + 24x + 48 - 10x + 32 = 0$
$3x^2 + 14x + 16 = 0$
$D = 7^2 - 3 * 16 = 49 - 48 = 1$
$x = \frac{-7 ± \sqrt{1}}{3}$
$x_1 = \frac{-7 - 1}{3} = \frac{-8}{3} = -2\frac{2}{3}$
$x_2 = \frac{-7 + 1}{3} = \frac{-6}{3} = -2$
Ответ:
$x_1 = -2\frac{2}{3}$;
$x_2 = -2$.

$15x^2 + 17 = 15(x + 1)^2$
$15x^2 + 17 = 15(x^2 + 2x + 1)$
$15x^2 + 17 = 15x^2 + 30x + 15$
$15x^2 + 17 - 15x^2 - 30x - 15 = 0$
2 − 30x = 0
−30x = −2
$x = \frac{1}{15}$

$(x + 1)^2 = 7918 - 2x$
$x^2 + 2x + 1 - 7918 + 2x = 0$
$x^2 + 4x - 7917 = 0$
$D = 2^2 - 1 * (-7917) = 4 + 7917 = 7921$
$x = -2 ± \sqrt{7921} = -2 ± 89$
$x_1 = -2 - 89 = -91$
$x_2 = -2 + 89 = 87$
Ответ:
$x_1 = -91$;
$x_2 = 87$.

$(x + 2)^2 = 3131 - 2x$
$x^2 + 4x + 4 - 3131 + 2x = 0$
$x^2 + 6x - 3127 = 0$
$D = 3^2 - 1 * (-3127) = 9 + 3127 = 3136$
$x = -3 ± \sqrt{3136} = -3 ± 56$
$x_1 = -3 - 56 = -59$
$x_2 = -3 + 56 = 53$
Ответ:
$x_1 = -59$;
$x_2 = 53$.

$(x + 1)^2 = (2x - 1)^2$
$x^2 + 2x + 1 = 4x^2 - 4x + 1$
$x^2 + 2x + 1 - 4x^2 + 4x - 1 = 0$
$-3x^2 + 6x = 0$ |*(−1)
$3x^2 - 6x = 0$
3x(x − 2) = 0
3x = 0 или x − 2 = 0
x = 2
Ответ:
$x_1 = 0$;
$x_2 = 2$.

$(x - 2)^2 + 48 = (2 - 3x)^2$
$x^2 - 4x + 4 + 48 = 4 - 12x + 9x^2$
$x^2 - 4x + 52 - 4 + 12x - 9x^2 = 0$
$-8x^2 + 8x + 48 = 0$ |:(−8)
$x^2 - x - 6 = 0$
$D = 1^2 - 4 * 1 * (-6) = 1 + 24 = 25$
$x = \frac{1 ± \sqrt{25}}{2}$
$x_1 = \frac{1 - 5}{2} = \frac{-4}{2} = -2$
$x_2 = \frac{1 + 5}{2} = \frac{6}{2} = 3$
Ответ:
$x_1 = -2$;
$x_2 = 3$.