Here are the essential concepts you must grasp in order to answer the question correctly.
Exponential Functions and Negative Exponents
Negative exponents indicate the reciprocal of the base raised to the positive exponent. For example, x^(-1) is equivalent to 1/x, and x^(-2) is equivalent to 1/x^2. Understanding this concept is crucial for rewriting the equation in a more manageable form.
Recommended video:
Substitution Method
The substitution method involves replacing a variable or expression with another variable to simplify the equation. In this case, substituting u = x^(-1) can transform the original equation into a quadratic form, making it easier to solve.
Recommended video:
Choosing a Method to Solve Quadratics
Quadratic Equations
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0. Solutions can be found using factoring, completing the square, or the quadratic formula. Recognizing the transformed equation as quadratic is essential for applying these solution methods effectively.
Recommended video:
Introduction to Quadratic Equations