Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Equations
Polynomial equations are mathematical expressions that involve variables raised to whole number powers. In this case, the equation includes terms like (x+2)^4 and (x+2)^2, which are polynomials. Understanding how to manipulate and solve polynomial equations is essential for finding the values of x that satisfy the equation.
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Substitution Method
The substitution method involves replacing a complex expression with a single variable to simplify the equation. In this problem, letting y = (x+2)^2 can transform the equation into a more manageable form. This technique helps in solving higher-degree polynomial equations by reducing them to quadratic equations.
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Quadratic Formula
The quadratic formula is a tool used to find the roots of quadratic equations, which are in the form ax^2 + bx + c = 0. The formula is x = (-b ± √(b² - 4ac)) / (2a). Once the equation is simplified using substitution, applying the quadratic formula will yield the solutions for the variable, which can then be translated back to find the original variable x.
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