Check if it is quadratic . If quadratic, change to standard form and identify a, b and c. 2x²=7x

To determine if the given equation is quadratic and convert it to standard form, we need to follow a few steps. The given equation is:

\[ 2x^2 = 7x \]

### Step 1: Bring all terms to one side
Subtract \(7x\) from both sides to set the equation to zero:

\[ 2x^2 - 7x = 0 \]

### Step 2: Identify if the equation is quadratic
An equation is quadratic if it can be written in the form:

\[ ax^2 + bx + c = 0 \]

In this case, our equation is:

\[ 2x^2 - 7x = 0 \]

### Step 3: Confirm it is quadratic
This equation fits the quadratic form, where:
- \(a = 2\)
- \(b = -7\)
- \(c = 0\)

### Step 4: State the standard form and identify \(a\), \(b\), and \(c\)
The standard form of the equation is:

\[ 2x^2 - 7x + 0 = 0 \]

Here:
- \(a = 2\)
- \(b = -7\)
- \(c = 0\)

So, the given equation is quadratic, and it is already in standard form.

### Summary
The equation \(2x^2 = 7x\) is a quadratic equation. When rewritten in standard form, it is:

\[ 2x^2 - 7x + 0 = 0 \]

Where:
- \(a = 2\)
- \(b = -7\)
- \(c = 0\)

Would you like further details or have any questions?

Here are some related questions to explore further:

1. How do you solve the quadratic equation \(2x^2 - 7x = 0\)?
2. What is the quadratic formula, and how is it used?
3. What are the roots of the equation \(2x^2 - 7x = 0\)?
4. How do you factor a quadratic equation?
5. What is the discriminant, and what does it tell you about the roots of a quadratic equation?
6. Can a quadratic equation have complex roots?
7. How do you complete the square for a quadratic equation?
8. What are some real-life applications of quadratic equations?

**Tip:** When identifying the coefficients \(a\), \(b\), and \(c\) in a quadratic equation, make sure all terms are on one side of the equation set to zero. This helps in accurately determining the values and solving the equation.

Learn how to identify and solve the quadratic equation 2x^2 = 7x. Understand how to convert it into standard form and identify the coefficients a, b, and c. This problem explores fundamental concepts of quadratic equations, suitable for Grades 7-9 students.

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