What substitution should be used to rewrite 4x^12 + 5x^6 + 14 = 0 as a quadratic equation?

To rewrite the equation 4x¹² + 5x⁶ + 14 = 0 as a quadratic equation, we can use a substitution method that simplifies the terms. A suitable substitution in this case is to let y = x⁶.

Using this substitution, we can express the equation in terms of y:

• Since x¹² = (x⁶)² = y², we can rewrite 4x¹² as 4y².
• 5x⁶ will simply become 5y.

Thus, the equation transforms to:

4y² + 5y + 14 = 0

This is now a standard quadratic equation in the variable y. By substituting y = x⁶ back after solving for y, we can find the values for x.