Solve each equation. See Example 7. (x-3)^2/5 = 4

Key Concepts

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. They can be solved using various methods, including factoring, completing the square, or applying the quadratic formula. In this context, the equation involves a squared term, indicating that it can be treated as a quadratic equation once simplified.

Square Roots

Square roots are the values that, when multiplied by themselves, yield the original number. In solving equations involving squares, such as (x-3)^2, taking the square root of both sides is a common step. This process introduces both positive and negative solutions, which must be considered to find all possible values of x.

Isolating Variables

Isolating variables is a fundamental algebraic technique used to solve equations. It involves rearranging the equation to get the variable of interest (in this case, x) on one side and all other terms on the opposite side. This process often includes operations like addition, subtraction, multiplication, and division, allowing for a clearer path to finding the solution.