$(5x + 3)^2 = 5(x + 3)$
$25x^2 + 30x + 9 = 5x + 15$
$25x^2 + 25x - 6 = 0$|:25
$x^2 + x - \frac{6}{25} = 0$
$(x + \frac{6}{5})(x - \frac{1}{5}) = 0$
$x + \frac{6}{5} = 0$
$x = -\frac{6}{5} = -1\frac{1}{5}$
или
$x - \frac{1}{5} = 0$
$x = \frac{1}{5}$
Ответ:
$x_1 = -1\frac{1}{5}$;
$x_2 = \frac{1}{5}$.

$(3x + 10)^2 = 3(x + 10)$
$9x^2 + 60x + 100 = 3x + 30$
$9x^2 + 57x + 70 = 0$
$D = 57^2 - 4 * 9 * 70 = 3249 - 2520 = 729$
$x = \frac{-57 ± \sqrt{729}}{18}$
$x_1 = \frac{-57 - 27}{18} = \frac{-84}{18} = -\frac{14}{3} = -4\frac{2}{3}$
$x_2 = \frac{-57 + 27}{18} = \frac{-30}{18} = -\frac{5}{3} = -1\frac{2}{3}$
Ответ:
$x_1 = -4\frac{2}{3}$;
$x_2 = -1\frac{2}{3}$.

$(3x - 8)^2 = 3x^2 - 8x$
$9x^2 - 48x + 64 = 3x^2 - 8x$
$6x^2 - 40x + 64 = 0$
$3x^2 - 20x + 32 = 0$
(3x − 8)(x − 4) = 0
3x − 8 = 0
3x = 8
$x = 2\frac{2}{3}$
или
x − 4
x = 4
Ответ:
$x_1 = 2\frac{2}{3}$;
$x_2 = 4$.

$(4x + 5)^2 = 5x^2 + 4x$
$16x^2 + 40x + 25 = 5x^2 + 4x$
$11x^2 + 36x + 25 = 0$
(11x + 25)(x + 1) = 0
11x + 25 = 0
11x = −25
$x = -\frac{25}{11} = -2\frac{3}{11}$
или
x + 1 = 0
x = −1
Ответ:
$x_1 = -2\frac{3}{11}$;
$x_2 = -1$.

$(5x + 3)^2 = 5x + 3$
$25x^2 + 30x + 9 = 5x + 3$
$25x^2 + 25x + 6 = 0$|:25
$x^2 + x + \frac{6}{25} = 0$
$(x + \frac{3}{5})(x + \frac{2}{5}) = 0$
$x + \frac{3}{5} = 0$
$x = -\frac{3}{5}$
или
$x + \frac{2}{5} = 0$
$x = -\frac{2}{5}$
Ответ:
$x_1 = -\frac{3}{5}$;
$x_2 = -\frac{2}{5}$.

$(5x + 3)^2 = (3x + 5)^2$
$25x^2 + 30x + 9 = 9x^2 + 30x + 25$
$16x^2 = 16$
$x^2 = 1$
x = ±1
Ответ:
$x_1 = -1$;
$x_2 = 1$.

$(4x + 5)^2 = 4(x + 5)^2$
$16x^2 + 40x + 25 = 4(x^2 + 10x + 25)$
$12x^2 = 75$
$4x^2 = 25$
$x^2 = \frac{25}{4} = (\frac{5}{2})^2$
x = ±2,5
Ответ:
$x_1 = -2,5$;
$x_2 = 2,5$.

$(2x + 10)^2 = 4(x + 5)^2$
$4x^2 + 40x + 100 = 4(x^2 + 10x + 25)$
$4(x^2 + 10x + 25) = 4(x^2 + 10x + 25)$
0 = 0
Ответ:
x ∈ R − равенство верно при любых x.