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What is the process called, something that start with manipulating

The image seems to involve solving a quadratic equation. Based on the content and steps, the handwritten note refers to a process where a quadratic equation is made easier to solve by manipulating it into a standard form (with a positive leading coefficient). This process is typically referred to as **"manipulating the equation"** or, more formally, **"manipulating the quadratic equation into standard form."**

The specific step where the equation's signs are adjusted to make the leading coefficient positive (changing the signs of the terms) is known as **"standardizing the quadratic equation"** or **"manipulating for simplicity"**. If you're seeking a name that begins with "manipulating," the term **"manipulating the equation"** could apply here.

Would you like a more detailed explanation of this process?

Here are 5 related questions that could expand your understanding:
1. What are the steps to convert any quadratic equation into standard form?
2. How does completing the square relate to manipulating a quadratic equation?
3. What are the conditions for solving a quadratic equation using the quadratic formula?
4. Can quadratic equations always be manipulated into a simpler form?
5. How can you factor a quadratic equation effectively once it's in standard form?

**Tip:** When solving quadratic equations, always aim to get a positive leading term for clarity and simplicity in further steps like factoring or applying the quadratic formula.

Find a number x such that (x+1)/(x-2) = 3x(x-2)

Learn how to solve a quadratic equation derived from the rational equation (x+1)/(x-2) = 3x(x-2) using cross-multiplication, expansion, and simplification. This example walks through converting the equation to standard quadratic form, suitable for students in Grades 9-11.

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