求解 sqrt{3}X-x-4/tan36^circ=16.4

$$\sqrt { 3 } X - \frac { x - 4 } { \tan 36 ^ { \circ } } = 16.4$$

求解 X 的值

$$X=\frac{2\sqrt{3}\left(3125000000000000x+24735304560274741\right)}{13622672400100515}$$

求解线性方程的步骤

对题中的三角函数求值

$$\sqrt{3} X - \frac{x - 4}{0.7265425280053608} = 16.4$$

x-4 的每项除以 0.7265425280053608 得 \frac{x}{0.7265425280053608}+\frac{-4}{0.7265425280053608}。

$$\sqrt{3}X-\left(\frac{x}{0.7265425280053608}+\frac{-4}{0.7265425280053608}\right)=16.4$$

将分子和分母同时乘以 10000000000000000 以展开 \frac{-4}{0.7265425280053608}。

$$\sqrt{3}X-\left(\frac{x}{0.7265425280053608}+\frac{-40000000000000000}{7265425280053608}\right)=16.4$$

通过求根和消去 8，将分数 \frac{-40000000000000000}{7265425280053608} 降低为最简分数。

$$\sqrt{3}X-\left(\frac{x}{0.7265425280053608}-\frac{5000000000000000}{908178160006701}\right)=16.4$$

要查找 \frac{x}{0.7265425280053608}-\frac{5000000000000000}{908178160006701} 的相反数，请查找每一项的相反数。

$$\sqrt{3}X-\frac{x}{0.7265425280053608}+\frac{5000000000000000}{908178160006701}=16.4$$

将 \frac{x}{0.7265425280053608} 添加到两侧。

$$\sqrt{3}X+\frac{5000000000000000}{908178160006701}=16.4+\frac{x}{0.7265425280053608}$$

将方程式两边同时减去 \frac{5000000000000000}{908178160006701}。

$$\sqrt{3}X=16.4+\frac{x}{0.7265425280053608}-\frac{5000000000000000}{908178160006701}$$

将 16.4 减去 \frac{5000000000000000}{908178160006701}，得到 \frac{49470609120549482}{4540890800033505}。

$$\sqrt{3}X=\frac{49470609120549482}{4540890800033505}+\frac{x}{0.7265425280053608}$$

该公式采用标准形式。

$$\sqrt{3}X=\frac{1250000000000000x}{908178160006701}+\frac{49470609120549482}{4540890800033505}$$

两边同时除以 \sqrt{3}。

$$\frac{\sqrt{3}X}{\sqrt{3}}=\frac{\frac{1250000000000000x}{908178160006701}+\frac{49470609120549482}{4540890800033505}}{\sqrt{3}}$$

除以 \sqrt{3} 是乘以 \sqrt{3} 的逆运算。

$$X=\frac{\frac{1250000000000000x}{908178160006701}+\frac{49470609120549482}{4540890800033505}}{\sqrt{3}}$$

\frac{49470609120549482}{4540890800033505}+\frac{1250000000000000x}{908178160006701} 除以 \sqrt{3}。

$$X=\frac{2\sqrt{3}\left(3125000000000000x+24735304560274741\right)}{13622672400100515}$$

求解 x 的值

$$x=\frac{908178160006701\sqrt{3}X}{1250000000000000}-7.91529745928791712$$