Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $60x$, the least common multiple of $30,4,x$.
$$2x\times 50=15x\times 10\times \frac{200}{x}$$
Multiply $2$ and $50$ to get $100$.
$$100x=15x\times 10\times \frac{200}{x}$$
Multiply $15$ and $10$ to get $150$.
$$100x=150x\times \frac{200}{x}$$
Express $150\times \frac{200}{x}$ as a single fraction.
$$100x=\frac{150\times 200}{x}x$$
Multiply $150$ and $200$ to get $30000$.
$$100x=\frac{30000}{x}x$$
Express $\frac{30000}{x}x$ as a single fraction.
$$100x=\frac{30000x}{x}$$
Subtract $\frac{30000x}{x}$ from both sides.
$$100x-\frac{30000x}{x}=0$$
To add or subtract expressions, expand them to make their denominators the same. Multiply $100x$ times $\frac{x}{x}$.
$$\frac{100xx}{x}-\frac{30000x}{x}=0$$
Since $\frac{100xx}{x}$ and $\frac{30000x}{x}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{100xx-30000x}{x}=0$$
Do the multiplications in $100xx-30000x$.
$$\frac{100x^{2}-30000x}{x}=0$$
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.
$$100x^{2}-30000x=0$$
Factor out $x$.
$$x\left(100x-30000\right)=0$$
To find equation solutions, solve $x=0$ and $100x-30000=0$.
$$x=0$$ $$x=300$$
Variable $x$ cannot be equal to $0$.
$$x=300$$
Steps Using the Quadratic Formula
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $60x$, the least common multiple of $30,4,x$.
$$2x\times 50=15x\times 10\times \frac{200}{x}$$
Multiply $2$ and $50$ to get $100$.
$$100x=15x\times 10\times \frac{200}{x}$$
Multiply $15$ and $10$ to get $150$.
$$100x=150x\times \frac{200}{x}$$
Express $150\times \frac{200}{x}$ as a single fraction.
$$100x=\frac{150\times 200}{x}x$$
Multiply $150$ and $200$ to get $30000$.
$$100x=\frac{30000}{x}x$$
Express $\frac{30000}{x}x$ as a single fraction.
$$100x=\frac{30000x}{x}$$
Subtract $\frac{30000x}{x}$ from both sides.
$$100x-\frac{30000x}{x}=0$$
To add or subtract expressions, expand them to make their denominators the same. Multiply $100x$ times $\frac{x}{x}$.
$$\frac{100xx}{x}-\frac{30000x}{x}=0$$
Since $\frac{100xx}{x}$ and $\frac{30000x}{x}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{100xx-30000x}{x}=0$$
Do the multiplications in $100xx-30000x$.
$$\frac{100x^{2}-30000x}{x}=0$$
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.
$$100x^{2}-30000x=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $100$ for $a$, $-30000$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
Now solve the equation $x=\frac{30000±30000}{200}$ when $±$ is plus. Add $30000$ to $30000$.
$$x=\frac{60000}{200}$$
Divide $60000$ by $200$.
$$x=300$$
Now solve the equation $x=\frac{30000±30000}{200}$ when $±$ is minus. Subtract $30000$ from $30000$.
$$x=\frac{0}{200}$$
Divide $0$ by $200$.
$$x=0$$
The equation is now solved.
$$x=300$$ $$x=0$$
Variable $x$ cannot be equal to $0$.
$$x=300$$
Steps for Completing the Square
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $60x$, the least common multiple of $30,4,x$.
$$2x\times 50=15x\times 10\times \frac{200}{x}$$
Multiply $2$ and $50$ to get $100$.
$$100x=15x\times 10\times \frac{200}{x}$$
Multiply $15$ and $10$ to get $150$.
$$100x=150x\times \frac{200}{x}$$
Express $150\times \frac{200}{x}$ as a single fraction.
$$100x=\frac{150\times 200}{x}x$$
Multiply $150$ and $200$ to get $30000$.
$$100x=\frac{30000}{x}x$$
Express $\frac{30000}{x}x$ as a single fraction.
$$100x=\frac{30000x}{x}$$
Subtract $\frac{30000x}{x}$ from both sides.
$$100x-\frac{30000x}{x}=0$$
To add or subtract expressions, expand them to make their denominators the same. Multiply $100x$ times $\frac{x}{x}$.
$$\frac{100xx}{x}-\frac{30000x}{x}=0$$
Since $\frac{100xx}{x}$ and $\frac{30000x}{x}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{100xx-30000x}{x}=0$$
Do the multiplications in $100xx-30000x$.
$$\frac{100x^{2}-30000x}{x}=0$$
Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $x$.
$$100x^{2}-30000x=0$$
Divide both sides by $100$.
$$\frac{100x^{2}-30000x}{100}=\frac{0}{100}$$
Dividing by $100$ undoes the multiplication by $100$.
Divide $-300$, the coefficient of the $x$ term, by $2$ to get $-150$. Then add the square of $-150$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
