Solving the Equation 0.5y - 0.2y 0.3y^2

When you encounter an algebraic equation, it is essential to break down and simplify it step by step to find the solution. In this article, we will solve the equation 0.5y - 0.2y 0.3y^2. This problem involves combining like terms, isolating the variable, and solving for the unknown variable y.

Step-by-Step Solution

Step 1: Combine Like Terms

First, we combine like terms on the left side of the equation 0.5y - 0.2y 0.3y^2. The like terms are 0.5y and 0.2y. Combining these, we get:

0.5y - 0.2y 0.3y^2

0.7y 0.3y^2

Step 2: Isolate the Variable y

Next, we move the term 0.3y^2 to the right side of the equation by subtracting it from both sides:

0.7y - 0.3y^2 0

This simplifies to:

0.7y 0.3y^2

Step 3: Solve for y

To solve for y, we can first rearrange the equation to get all terms on one side:

0.7y - 0.3y^2 0

Using the distributive property, we can factor out y:

0.3y^2 - 0.7y 0

This is a quadratic equation, but in this case, it can be solved by factoring or division:

0.3y^2 - 0.7y 0

0.3y(y - 2/0.3) 0

0.3y(y - 2.3333) 0

Since the product of these terms is zero, one of the factors must be zero:

0.3y 0

y - 2.3333 0

Solving for y, we get:

y 0

y 2.3333

However, upon closer inspection, the second solution can be simplified. We can simplify the fraction 2.3333 to:

y 5

Conclusion

The solution to the equation 0.5y - 0.2y 0.3y^2 is:

y 5

Additional Examples and Further Reading

For further practice, you can solve similar equations like:

0.3y 0.4y 1.25y^2 0.6y - 0.9y 1.5y^2

By following the same steps of combining like terms, isolating the variable, and solving the resulting quadratic or linear equation, you can find the solutions.