Quadratic equations, a fundamental concept in algebra, involve equations with variables raised to the power of 2. One of the most common types of quadratic equations is the pure quadratic equation. In this blog post, we will explore the steps to solve a pure quadratic equation and provide you with a clear understanding of the process.

What is a Pure Quadratic Equation?

A pure quadratic equation is a quadratic equation that does not include any cross-product term or a term with a power other than 2. It has the form:

ax^2 + bx + c = 0

Where a, b, and c are constants, and x is the unknown variable.

Steps to Solve a Pure Quadratic Equation

Solving a pure quadratic equation involves a series of steps that allow us to find the values of x that satisfy the equation. Let’s take a look at the process:

  1. First, ensure that the equation is in the standard form: ax^2 + bx + c = 0. If not, rearrange the terms.
  2. Next, identify the values of a, b, and c in the equation. These values are crucial for further calculations.
  3. Use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a).
  4. Plug in the values of a, b, and c into the quadratic formula.
  5. Simplify the equation obtained in the previous step using basic arithmetic operations.
  6. Apply the square root to any simplified expression under the square root sign.
  7. Finally, solve for x by considering the positive and negative square root values obtained.

Example:

Let’s work through an example to solidify the understanding of solving a pure quadratic equation:

Given the equation: 3x^2 – 10x + 6 = 0

After identifying the values of a, b, and c as 3, -10, and 6 respectively, we can apply the quadratic formula:

x = (-(-10) ± √((-10)² – 4 * 3 * 6)) / (2 * 3)

By simplifying the equation further, we obtain:

x = (10 ± √(100 – 72)) / 6

After performing the arithmetic, we have:

x = (10 ± √28) / 6

Now, simplifying the expression under the square root, we get:

x = (10 ± 2√7) / 6

We can further simplify the expression by dividing both the numerator and the denominator by 2:

x = (5 ± √7) / 3

Thus, the solutions for the given pure quadratic equation are (5 + √7) / 3 and (5 – √7) / 3.

By following these steps, you can successfully solve a pure quadratic equation and find the values of x that satisfy the equation.

Remember, practice is key to mastering quadratic equations. Regularly solving different types of quadratic equations will enhance your problem-solving skills and build a strong foundation in algebra.

We hope this blog post has provided you with a comprehensive guide on how to solve a pure quadratic equation. Feel free to leave any comments or questions below.

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