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The given equation is:

\[
4x^2 = 2x - 3
\]

To express this in standard quadratic form \(ax^2 + bx + c = 0\), we need to move all terms to one side of the equation:

\[
4x^2 - 2x + 3 = 0
\]

Now, we can identify the coefficients:

- \(a = 4\) (coefficient of \(x^2\))
- \(b = -2\) (coefficient of \(x\))
- \(c = 3\) (constant term)

The question asks for the value of \(b\), which is the coefficient of \(x\). Therefore, the value of \(b\) is:

\[
b = -2
\]

The correct answer is \(-2\).

Would you like any further details or explanation?

Here are five related questions for further exploration:
1. How do you find the discriminant of a quadratic equation?
2. What are the roots of the quadratic equation \(4x^2 - 2x - 3 = 0\)?
3. What is the sum of the roots of this quadratic equation?
4. What is the significance of the \(b^2 - 4ac\) term in quadratic equations?
5. Can a quadratic equation have complex roots, and how can we identify them?

**Tip**: Always remember to write quadratic equations in standard form before identifying coefficients.

In the quadratic equation 4x^2 = 2x - 3, what is the value of b?

Learn how to solve the quadratic equation 4x^2 = 2x - 3 and find the value of b. This detailed step-by-step solution covers key algebraic concepts such as the quadratic equation formula. Ideal for students in Grades 7-9.

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