How can we rewrite the expression 4x^12 + 5x^6 + 14 = 0 as a quadratic equation?

To rewrite the expression 4x¹² + 5x⁶ + 14 = 0 as a quadratic equation, we need to use a substitution that simplifies the terms.

Let’s introduce a new variable, say y, where we define it as:

y = x⁶

With this substitution, we can express:

• x¹² = (x⁶)² = y²
• x⁶ = y

Now we can rewrite the original expression as:

4y² + 5y + 14 = 0

This is now in the standard form of a quadratic equation, which is structured as Ay² + By + C = 0, where A = 4, B = 5, and C = 14.

In summary, by substituting y = x⁶, we successfully transformed the original expression into a quadratic equation:

4y² + 5y + 14 = 0