Solve x * (1 + R/100) ^ 2 - x = (xR * 4)/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

$$x(1+\frac{R}{100})^{2}-x=\frac{x\times R\times4}{100}$$

Solve for x (complex solution)

$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&R=200\text{ or }R=0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $100$.

$$100x\left(1+\frac{R}{100}\right)^{2}-100x=xR\times 4$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(1+\frac{R}{100}\right)^{2}$.

$$100x\left(1+2\times \frac{R}{100}+\left(\frac{R}{100}\right)^{2}\right)-100x=xR\times 4$$

Cancel out $100$, the greatest common factor in $2$ and $100$.

$$100x\left(1+\frac{R}{50}+\left(\frac{R}{100}\right)^{2}\right)-100x=xR\times 4$$

To raise $\frac{R}{100}$ to a power, raise both numerator and denominator to the power and then divide.

$$100x\left(1+\frac{R}{50}+\frac{R^{2}}{100^{2}}\right)-100x=xR\times 4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{100^{2}}{100^{2}}$.

$$100x\left(\frac{100^{2}}{100^{2}}+\frac{R}{50}+\frac{R^{2}}{100^{2}}\right)-100x=xR\times 4$$

Since $\frac{100^{2}}{100^{2}}$ and $\frac{R^{2}}{100^{2}}$ have the same denominator, add them by adding their numerators.

$$100x\left(\frac{100^{2}+R^{2}}{100^{2}}+\frac{R}{50}\right)-100x=xR\times 4$$

Combine like terms in $100^{2}+R^{2}$.

$$100x\left(\frac{10000+R^{2}}{100^{2}}+\frac{R}{50}\right)-100x=xR\times 4$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $100^{2}$ and $50$ is $10000$. Multiply $\frac{R}{50}$ times $\frac{200}{200}$.

$$100x\left(\frac{10000+R^{2}}{10000}+\frac{200R}{10000}\right)-100x=xR\times 4$$

Since $\frac{10000+R^{2}}{10000}$ and $\frac{200R}{10000}$ have the same denominator, add them by adding their numerators.

$$100x\times \frac{10000+R^{2}+200R}{10000}-100x=xR\times 4$$

Cancel out $10000$, the greatest common factor in $100$ and $10000$.

$$\frac{10000+R^{2}+200R}{100}x-100x=xR\times 4$$

Divide each term of $10000+R^{2}+200R$ by $100$ to get $100+\frac{1}{100}R^{2}+2R$.

$$\left(100+\frac{1}{100}R^{2}+2R\right)x-100x=xR\times 4$$

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

$$100x+\frac{1}{100}R^{2}x+2Rx-100x=xR\times 4$$

Combine $100x$ and $-100x$ to get $0$.

$$\frac{1}{100}R^{2}x+2Rx=xR\times 4$$

Subtract $xR\times 4$ from both sides.

$$\frac{1}{100}R^{2}x+2Rx-xR\times 4=0$$

Combine $2Rx$ and $-xR\times 4$ to get $-2Rx$.

$$\frac{1}{100}R^{2}x-2Rx=0$$

Combine all terms containing $x$.

$$\left(\frac{1}{100}R^{2}-2R\right)x=0$$

The equation is in standard form.

$$\left(\frac{R^{2}}{100}-2R\right)x=0$$

Divide $0$ by $\frac{1}{100}R^{2}-2R$.

$$x=0$$

Solve for x

$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&R=200\text{ or }R=0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $100$.

$$100x\left(1+\frac{R}{100}\right)^{2}-100x=xR\times 4$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(1+\frac{R}{100}\right)^{2}$.

$$100x\left(1+2\times \frac{R}{100}+\left(\frac{R}{100}\right)^{2}\right)-100x=xR\times 4$$

Cancel out $100$, the greatest common factor in $2$ and $100$.

$$100x\left(1+\frac{R}{50}+\left(\frac{R}{100}\right)^{2}\right)-100x=xR\times 4$$

To raise $\frac{R}{100}$ to a power, raise both numerator and denominator to the power and then divide.

$$100x\left(1+\frac{R}{50}+\frac{R^{2}}{100^{2}}\right)-100x=xR\times 4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{100^{2}}{100^{2}}$.

$$100x\left(\frac{100^{2}}{100^{2}}+\frac{R}{50}+\frac{R^{2}}{100^{2}}\right)-100x=xR\times 4$$

Since $\frac{100^{2}}{100^{2}}$ and $\frac{R^{2}}{100^{2}}$ have the same denominator, add them by adding their numerators.

$$100x\left(\frac{100^{2}+R^{2}}{100^{2}}+\frac{R}{50}\right)-100x=xR\times 4$$

Combine like terms in $100^{2}+R^{2}$.

$$100x\left(\frac{10000+R^{2}}{100^{2}}+\frac{R}{50}\right)-100x=xR\times 4$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $100^{2}$ and $50$ is $10000$. Multiply $\frac{R}{50}$ times $\frac{200}{200}$.

$$100x\left(\frac{10000+R^{2}}{10000}+\frac{200R}{10000}\right)-100x=xR\times 4$$

Since $\frac{10000+R^{2}}{10000}$ and $\frac{200R}{10000}$ have the same denominator, add them by adding their numerators.

$$100x\times \frac{10000+R^{2}+200R}{10000}-100x=xR\times 4$$

Cancel out $10000$, the greatest common factor in $100$ and $10000$.

$$\frac{10000+R^{2}+200R}{100}x-100x=xR\times 4$$

Divide each term of $10000+R^{2}+200R$ by $100$ to get $100+\frac{1}{100}R^{2}+2R$.

$$\left(100+\frac{1}{100}R^{2}+2R\right)x-100x=xR\times 4$$

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

$$100x+\frac{1}{100}R^{2}x+2Rx-100x=xR\times 4$$

Combine $100x$ and $-100x$ to get $0$.

$$\frac{1}{100}R^{2}x+2Rx=xR\times 4$$

Subtract $xR\times 4$ from both sides.

$$\frac{1}{100}R^{2}x+2Rx-xR\times 4=0$$

Combine $2Rx$ and $-xR\times 4$ to get $-2Rx$.

$$\frac{1}{100}R^{2}x-2Rx=0$$

Combine all terms containing $x$.

$$\left(\frac{1}{100}R^{2}-2R\right)x=0$$

The equation is in standard form.

$$\left(\frac{R^{2}}{100}-2R\right)x=0$$

Divide $0$ by $\frac{1}{100}R^{2}-2R$.

$$x=0$$

Solve for R (complex solution)

$\left\{\begin{matrix}\\R=200\text{; }R=0\text{, }&\text{unconditionally}\\R\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$

Solve for R

$\left\{\begin{matrix}\\R=200\text{; }R=0\text{, }&\text{unconditionally}\\R\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$