Solve (BC)/(sqrt(3)) = (BC)/(p + 100) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{BC}{\sqrt{3}}=\frac{BC}{p+100}$$

Solve for B (complex solution)

$\left\{\begin{matrix}B=0\text{, }&p\neq -100\\B\in \mathrm{C}\text{, }&p=\sqrt{3}-100\text{ or }\left(C=0\text{ and }p\neq -100\right)\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $p+100$.

$$\frac{1}{3}\left(p+100\right)\times 3^{\frac{1}{2}}BC=BC$$

Use the distributive property to multiply $\frac{1}{3}$ by $p+100$.

$$\left(\frac{1}{3}p+\frac{100}{3}\right)\times 3^{\frac{1}{2}}BC=BC$$

Use the distributive property to multiply $\frac{1}{3}p+\frac{100}{3}$ by $3^{\frac{1}{2}}$.

$$\left(\frac{1}{3}p\times 3^{\frac{1}{2}}+\frac{100}{3}\times 3^{\frac{1}{2}}\right)BC=BC$$

Use the distributive property to multiply $\frac{1}{3}p\times 3^{\frac{1}{2}}+\frac{100}{3}\times 3^{\frac{1}{2}}$ by $B$.

$$\left(\frac{1}{3}p\times 3^{\frac{1}{2}}B+\frac{100}{3}\times 3^{\frac{1}{2}}B\right)C=BC$$

Use the distributive property to multiply $\frac{1}{3}p\times 3^{\frac{1}{2}}B+\frac{100}{3}\times 3^{\frac{1}{2}}B$ by $C$.

$$\frac{1}{3}p\times 3^{\frac{1}{2}}BC+\frac{100}{3}\times 3^{\frac{1}{2}}BC=BC$$

Subtract $BC$ from both sides.

$$\frac{1}{3}p\times 3^{\frac{1}{2}}BC+\frac{100}{3}\times 3^{\frac{1}{2}}BC-BC=0$$

Reorder the terms.

$$\frac{1}{3}\sqrt{3}BCp+\frac{100}{3}\sqrt{3}BC-BC=0$$

Combine all terms containing $B$.

$$\left(\frac{1}{3}\sqrt{3}Cp+\frac{100}{3}\sqrt{3}C-C\right)B=0$$

The equation is in standard form.

$$\left(\frac{\sqrt{3}Cp}{3}+\frac{100\sqrt{3}C}{3}-C\right)B=0$$

Divide $0$ by $\frac{1}{3}\sqrt{3}Cp+\frac{100}{3}\sqrt{3}C-C$.

$$B=0$$

Solve for C (complex solution)

$\left\{\begin{matrix}C=0\text{, }&p\neq -100\\C\in \mathrm{C}\text{, }&p=\sqrt{3}-100\text{ or }\left(B=0\text{ and }p\neq -100\right)\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $p+100$.

$$\frac{1}{3}\left(p+100\right)\times 3^{\frac{1}{2}}BC=BC$$

Use the distributive property to multiply $\frac{1}{3}$ by $p+100$.

$$\left(\frac{1}{3}p+\frac{100}{3}\right)\times 3^{\frac{1}{2}}BC=BC$$

Use the distributive property to multiply $\frac{1}{3}p+\frac{100}{3}$ by $3^{\frac{1}{2}}$.

$$\left(\frac{1}{3}p\times 3^{\frac{1}{2}}+\frac{100}{3}\times 3^{\frac{1}{2}}\right)BC=BC$$

Use the distributive property to multiply $\frac{1}{3}p\times 3^{\frac{1}{2}}+\frac{100}{3}\times 3^{\frac{1}{2}}$ by $B$.

$$\left(\frac{1}{3}p\times 3^{\frac{1}{2}}B+\frac{100}{3}\times 3^{\frac{1}{2}}B\right)C=BC$$

Use the distributive property to multiply $\frac{1}{3}p\times 3^{\frac{1}{2}}B+\frac{100}{3}\times 3^{\frac{1}{2}}B$ by $C$.

$$\frac{1}{3}p\times 3^{\frac{1}{2}}BC+\frac{100}{3}\times 3^{\frac{1}{2}}BC=BC$$

Subtract $BC$ from both sides.

$$\frac{1}{3}p\times 3^{\frac{1}{2}}BC+\frac{100}{3}\times 3^{\frac{1}{2}}BC-BC=0$$

Reorder the terms.

$$\frac{1}{3}\sqrt{3}BCp+\frac{100}{3}\sqrt{3}BC-BC=0$$

Combine all terms containing $C$.

$$\left(\frac{1}{3}\sqrt{3}Bp+\frac{100}{3}\sqrt{3}B-B\right)C=0$$

The equation is in standard form.

$$\left(\frac{\sqrt{3}Bp}{3}+\frac{100\sqrt{3}B}{3}-B\right)C=0$$

Divide $0$ by $\frac{1}{3}\sqrt{3}Bp+\frac{100}{3}\sqrt{3}B-B$.

$$C=0$$

Solve for B

$\left\{\begin{matrix}B=0\text{, }&p\neq -100\\B\in \mathrm{R}\text{, }&p=\sqrt{3}-100\text{ or }\left(C=0\text{ and }p\neq -100\right)\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $p+100$.

$$\frac{1}{3}\left(p+100\right)\times 3^{\frac{1}{2}}BC=BC$$

Use the distributive property to multiply $\frac{1}{3}$ by $p+100$.

$$\left(\frac{1}{3}p+\frac{100}{3}\right)\times 3^{\frac{1}{2}}BC=BC$$

Use the distributive property to multiply $\frac{1}{3}p+\frac{100}{3}$ by $3^{\frac{1}{2}}$.

$$\left(\frac{1}{3}p\times 3^{\frac{1}{2}}+\frac{100}{3}\times 3^{\frac{1}{2}}\right)BC=BC$$

Use the distributive property to multiply $\frac{1}{3}p\times 3^{\frac{1}{2}}+\frac{100}{3}\times 3^{\frac{1}{2}}$ by $B$.

$$\left(\frac{1}{3}p\times 3^{\frac{1}{2}}B+\frac{100}{3}\times 3^{\frac{1}{2}}B\right)C=BC$$

Use the distributive property to multiply $\frac{1}{3}p\times 3^{\frac{1}{2}}B+\frac{100}{3}\times 3^{\frac{1}{2}}B$ by $C$.

$$\frac{1}{3}p\times 3^{\frac{1}{2}}BC+\frac{100}{3}\times 3^{\frac{1}{2}}BC=BC$$

Subtract $BC$ from both sides.

$$\frac{1}{3}p\times 3^{\frac{1}{2}}BC+\frac{100}{3}\times 3^{\frac{1}{2}}BC-BC=0$$

Reorder the terms.

$$\frac{1}{3}\sqrt{3}BCp+\frac{100}{3}\sqrt{3}BC-BC=0$$

Combine all terms containing $B$.

$$\left(\frac{1}{3}\sqrt{3}Cp+\frac{100}{3}\sqrt{3}C-C\right)B=0$$

The equation is in standard form.

$$\left(\frac{\sqrt{3}Cp}{3}+\frac{100\sqrt{3}C}{3}-C\right)B=0$$

Divide $0$ by $\frac{1}{3}\sqrt{3}Cp+\frac{100}{3}\sqrt{3}C-C$.

$$B=0$$

Solve for C

$\left\{\begin{matrix}C=0\text{, }&p\neq -100\\C\in \mathrm{R}\text{, }&p=\sqrt{3}-100\text{ or }\left(B=0\text{ and }p\neq -100\right)\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $p+100$.

$$\frac{1}{3}\left(p+100\right)\times 3^{\frac{1}{2}}BC=BC$$

Use the distributive property to multiply $\frac{1}{3}$ by $p+100$.

$$\left(\frac{1}{3}p+\frac{100}{3}\right)\times 3^{\frac{1}{2}}BC=BC$$

Use the distributive property to multiply $\frac{1}{3}p+\frac{100}{3}$ by $3^{\frac{1}{2}}$.

$$\left(\frac{1}{3}p\times 3^{\frac{1}{2}}+\frac{100}{3}\times 3^{\frac{1}{2}}\right)BC=BC$$

Use the distributive property to multiply $\frac{1}{3}p\times 3^{\frac{1}{2}}+\frac{100}{3}\times 3^{\frac{1}{2}}$ by $B$.

$$\left(\frac{1}{3}p\times 3^{\frac{1}{2}}B+\frac{100}{3}\times 3^{\frac{1}{2}}B\right)C=BC$$

Use the distributive property to multiply $\frac{1}{3}p\times 3^{\frac{1}{2}}B+\frac{100}{3}\times 3^{\frac{1}{2}}B$ by $C$.

$$\frac{1}{3}p\times 3^{\frac{1}{2}}BC+\frac{100}{3}\times 3^{\frac{1}{2}}BC=BC$$

Subtract $BC$ from both sides.

$$\frac{1}{3}p\times 3^{\frac{1}{2}}BC+\frac{100}{3}\times 3^{\frac{1}{2}}BC-BC=0$$

Reorder the terms.

$$\frac{1}{3}\sqrt{3}BCp+\frac{100}{3}\sqrt{3}BC-BC=0$$

Combine all terms containing $C$.

$$\left(\frac{1}{3}\sqrt{3}Bp+\frac{100}{3}\sqrt{3}B-B\right)C=0$$

The equation is in standard form.

$$\left(\frac{\sqrt{3}Bp}{3}+\frac{100\sqrt{3}B}{3}-B\right)C=0$$

Divide $0$ by $\frac{1}{3}\sqrt{3}Bp+\frac{100}{3}\sqrt{3}B-B$.

$$C=0$$