Solve X * (1 + r/100) ^ 2 - X = (xxr * 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

$$X(1+\frac{r}{100})^{2}-X=\frac{xxr\times4}{100}$$

Solve for X (complex solution)

$\left\{\begin{matrix}X=\frac{400x^{2}}{r+200}\text{, }&r\neq -200\\X\in \mathrm{C}\text{, }&r=0\text{ or }\left(x=0\text{ and }r=-200\right)\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $100$.

$$100X\left(1+\frac{r}{100}\right)^{2}-100X=xxr\times 4$$

Multiply $x$ and $x$ to get $x^{2}$.

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

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

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

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

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

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

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

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

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

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

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

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

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

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 $\frac{200}{200}$.

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

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

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

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

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

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

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

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

$$100X+\frac{1}{100}r^{2}X+2rX-100X=x^{2}r\times 4$$

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

$$\frac{1}{100}r^{2}X+2rX=x^{2}r\times 4$$

Combine all terms containing $X$.

$$\left(\frac{1}{100}r^{2}+2r\right)X=x^{2}r\times 4$$

The equation is in standard form.

$$\left(\frac{r^{2}}{100}+2r\right)X=4rx^{2}$$

Divide both sides by $\frac{1}{100}r^{2}+2r$.

$$\frac{\left(\frac{r^{2}}{100}+2r\right)X}{\frac{r^{2}}{100}+2r}=\frac{4rx^{2}}{\frac{r^{2}}{100}+2r}$$

Dividing by $\frac{1}{100}r^{2}+2r$ undoes the multiplication by $\frac{1}{100}r^{2}+2r$.

$$X=\frac{4rx^{2}}{\frac{r^{2}}{100}+2r}$$

Divide $4x^{2}r$ by $\frac{1}{100}r^{2}+2r$.

$$X=\frac{400x^{2}}{r+200}$$

Solve for X

$\left\{\begin{matrix}X=\frac{400x^{2}}{r+200}\text{, }&r\neq -200\\X\in \mathrm{R}\text{, }&r=0\text{ or }\left(x=0\text{ and }r=-200\right)\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $100$.

$$100X\left(1+\frac{r}{100}\right)^{2}-100X=xxr\times 4$$

Multiply $x$ and $x$ to get $x^{2}$.

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

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

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

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

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

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

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

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

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

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

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

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

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

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 $\frac{200}{200}$.

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

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

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

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

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

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

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

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

$$100X+\frac{1}{100}r^{2}X+2rX-100X=x^{2}r\times 4$$

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

$$\frac{1}{100}r^{2}X+2rX=x^{2}r\times 4$$

Combine all terms containing $X$.

$$\left(\frac{1}{100}r^{2}+2r\right)X=x^{2}r\times 4$$

The equation is in standard form.

$$\left(\frac{r^{2}}{100}+2r\right)X=4rx^{2}$$

Divide both sides by $\frac{1}{100}r^{2}+2r$.

$$\frac{\left(\frac{r^{2}}{100}+2r\right)X}{\frac{r^{2}}{100}+2r}=\frac{4rx^{2}}{\frac{r^{2}}{100}+2r}$$

Dividing by $\frac{1}{100}r^{2}+2r$ undoes the multiplication by $\frac{1}{100}r^{2}+2r$.

$$X=\frac{4rx^{2}}{\frac{r^{2}}{100}+2r}$$

Divide $4x^{2}r$ by $\frac{1}{100}r^{2}+2r$.

$$X=\frac{400x^{2}}{r+200}$$

Solve for r (complex solution)

$\left\{\begin{matrix}\\r=0\text{, }&\text{unconditionally}\\r=\frac{400x^{2}}{X}-200\text{, }&X\neq 0\\r\in \mathrm{C}\text{, }&X=0\text{ and }x=0\end{matrix}\right.$

Solve for r

$\left\{\begin{matrix}\\r=0\text{, }&\text{unconditionally}\\r=\frac{400x^{2}}{X}-200\text{, }&X\neq 0\\r\in \mathrm{R}\text{, }&X=0\text{ and }x=0\end{matrix}\right.$