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 a polynomial in terms of (x-4), which is raised to the fourth power. 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 simpler variable to make solving easier. In this problem, letting y = (x-4)^2 simplifies the equation significantly, transforming it into a quadratic form. This technique is crucial for breaking down higher-degree polynomials into more manageable forms.
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Quadratic Formula
The quadratic formula is a tool used to find the roots of quadratic equations, expressed as x = (-b ± √(b²-4ac)) / 2a. Once the original equation is simplified into a quadratic form, applying this formula allows for the determination of the values of y, which can then be substituted back to find the corresponding x values.
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