次の方程式を解きます。 (1) $2x = -6x + 32$ (2) $6(1 - 4x) = 1 + 6x$ (3) $4(1 + x) = 6$ (4) $x^2 = 8$ (5) $5x^2 - 2x = 0$ (6) $x^2 - 3x - 10 = 0$ (7) $x^2 - 9 = 0$ (8) $5x^2 - 8x + 3 = 0$

1. 問題の内容

次の方程式を解きます。

(1) $2x = -6x + 32$

(2) $6(1 - 4x) = 1 + 6x$

(3) $4(1 + x) = 6$

(4) $x^2 = 8$

(5) $5x^2 - 2x = 0$

(6) $x^2 - 3x - 10 = 0$

(7) $x^2 - 9 = 0$

(8) $5x^2 - 8x + 3 = 0$

2. 解き方の手順

(1) $2x = -6x + 32$

$2x + 6x = 32$

$8x = 32$

$x = \frac{32}{8}$

$x = 4$

(2) $6(1 - 4x) = 1 + 6x$

$6 - 24x = 1 + 6x$

$6 - 1 = 6x + 24x$

$5 = 30x$

$x = \frac{5}{30}$

$x = \frac{1}{6}$

(3) $4(1 + x) = 6$

$4 + 4x = 6$

$4x = 6 - 4$

$4x = 2$

$x = \frac{2}{4}$

$x = \frac{1}{2}$

(4) $x^2 = 8$

$x = \pm \sqrt{8}$

$x = \pm 2\sqrt{2}$

(5) $5x^2 - 2x = 0$

$x(5x - 2) = 0$

$x = 0$ または $5x - 2 = 0$

$x = 0$ または $5x = 2$

$x = 0$ または $x = \frac{2}{5}$

(6) $x^2 - 3x - 10 = 0$

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

$x - 5 = 0$ または $x + 2 = 0$

$x = 5$ または $x = -2$

(7) $x^2 - 9 = 0$

$x^2 = 9$

$x = \pm \sqrt{9}$

$x = \pm 3$

(8) $5x^2 - 8x + 3 = 0$

$(5x - 3)(x - 1) = 0$

$5x - 3 = 0$ または $x - 1 = 0$

$5x = 3$ または $x = 1$

$x = \frac{3}{5}$ または $x = 1$

3. 最終的な答え

(1) $x = 4$

(2) $x = \frac{1}{6}$

(3) $x = \frac{1}{2}$

(4) $x = \pm 2\sqrt{2}$

(5) $x = 0, \frac{2}{5}$

(6) $x = 5, -2$

(7) $x = 3, -3$

(8) $x = \frac{3}{5}, 1$